Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D41 |
| commutator, socle, cosocle | C22×C41 | C24 |
| Fitting | #121×C41 | C2 |
| hypercenter | #121 | D41 |
| hypocenter | C41 | D42 |
| LCS | G ▷ C22×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D164 | C2 | semidirect |
| 2. C2×D4×D41 | C2 | semidirect |
| 3. C2×D4×D41 | C2 | semidirect |
| 4. #13050160 | C2 | semidirect |
| 5. #13050139 | C2 | semidirect |
| 6. #13050137 | C2 | semidirect |
| 7. #13050134 | C2 | semidirect |
| 8. #13050132 | C2 | semidirect |
| 9. #13050126 | C2 | semidirect |
| 10. C4×C22⋊D41 | C2 | semidirect |
| 11. #121×C41 | C2 | semidirect |
| 12. C23×D41 | C22 | semidirect |
| 13. C23×D41 | C22 | semidirect |
| 14. C2×D4×C41 | C22 | semidirect |
| 15. C2×D4×C41 | C22 | semidirect |
| 16. C22×C4×C41 | C22 | semidirect |
| 18. C2×C22⋊D41 | C22 | semidirect |
| 19. C2×C22⋊D41 | C22 | semidirect |
| 20. C2×C22⋊D41 | C22 | semidirect |
| 25. C2×D164 | C22 | semidirect |
| 26. C2×D164 | C22 | semidirect |
| 27. C2×D164 | C22 | semidirect |
| 28. C2×C4×D41 | C22 | semidirect |
| 29. C2×C4×D41 | C22 | semidirect |
| 30. C4⋊C4×C41 | C22 | semidirect |
| 31. C22⋊C4×C41 | C22 | semidirect |
| 32. C22⋊Dic41 | C22 | semidirect |
| 33. #10620281 | C22 | semidirect |
| 34. #10620281 | C22 | semidirect |
| 35. #10620281 | C22 | semidirect |
| 36. #10620279 | C22 | semidirect |
| 37. C4×Dic41 | C22 | semidirect |
| 58. C22⋊D41 | D4 | semidirect |
| 65. D164 | D4 | semidirect |
| 73. C22×C41 | C2×D4 | semidirect |
| 84. C2×D41 | C2×D4 | semidirect |
| 85. C2×D41 | C2×D4 | semidirect |
| 88. C4×C41 | C2×D4 | semidirect |
| 91. Dic41 | C2×D4 | semidirect |
| 101. C41 | D42 | semidirect |
| 108. #121 | D41 | semidirect |
| 126. C2×D4 | C2×D41 | semidirect |
| 127. C2×D4 | C2×D41 | semidirect |
| 130. C22×C4 | C2×D41 | semidirect |
| 132. C4⋊C4 | C2×D41 | semidirect |
| 137. C22⋊C4 | C2×D41 | semidirect |
| 185. C22 | D4×D41 | semidirect |
| 192. C4 | D4×D41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D164 | 2 |
| C2×D4×D41 | 2 |
| #13050160 | 2 |
| #13050139 | 2 |
| #13050137 | 2 |
| #13050134 | 2 |
| #13050132 | 2 |
| #13050126 | 2 |
| C4×C22⋊D41 | 2 |
| #121×C41 | 2 |
| D42 | 41 |