Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 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 | #123×C41 | C2 |
| hypercenter | #123 | D41 |
| hypocenter | C41 | #560 |
| LCS | G ▷ C22×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13050160 | C2 | semidirect |
| 2. #13050159 | C2 | semidirect |
| 3. #13050146 | C2 | semidirect |
| 4. #13050139 | C2 | semidirect |
| 5. #13050138 | C2 | semidirect |
| 6. #13050137 | C2 | semidirect |
| 7. #13050134 | C2 | semidirect |
| 8. #13050132 | C2 | semidirect |
| 9. #123×C41 | C2 | semidirect |
| 12. C22×C4×C41 | C22 | semidirect |
| 15. C2×C22⋊D41 | C22 | semidirect |
| 18. C2×D164 | C22 | semidirect |
| 19. C2×C4×D41 | C22 | semidirect |
| 20. C4⋊C4×C41 | C22 | semidirect |
| 22. C22⋊C4×C41 | C22 | semidirect |
| 27. #10620281 | C22 | semidirect |
| 28. C4⋊Dic41 | C22 | semidirect |
| 29. #10620279 | C22 | semidirect |
| 30. C4×Dic41 | C22 | semidirect |
| 75. C41 | #560 | semidirect |
| 79. #123 | D41 | semidirect |
| 94. C22×C4 | C2×D41 | semidirect |
| 97. C4⋊C4 | C2×D41 | semidirect |
| 104. C22⋊C4 | C2×D41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13050160 | 2 |
| #13050159 | 2 |
| #13050146 | 2 |
| #13050139 | 2 |
| #13050138 | 2 |
| #13050137 | 2 |
| #13050134 | 2 |
| #13050132 | 2 |
| #123×C41 | 2 |
| #560 | 41 |