Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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 | #127×C41 | C2 |
| hypercenter | #127 | D41 |
| hypocenter | C41 | #535 |
| LCS | G ▷ C22×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10620308 | C2 | semidirect |
| 2. C2×D4×D41 | C2 | semidirect |
| 3. #13050160 | C2 | semidirect |
| 4. #13050152 | C2 | semidirect |
| 5. #13050151 | C2 | semidirect |
| 6. #13050136 | C2 | semidirect |
| 7. #13050132 | C2 | semidirect |
| 8. #13050121 | C2 | semidirect |
| 9. #127×C41 | C2 | semidirect |
| 12. C2×D4×C41 | C22 | semidirect |
| 13. C2×D4×C41 | C22 | semidirect |
| 16. C2×C22⋊D41 | C22 | semidirect |
| 17. C22×Dic41 | C22 | semidirect |
| 22. C2×Dic82 | C22 | semidirect |
| 23. C42×C41 | C22 | semidirect |
| 24. C22⋊Dic41 | C22 | semidirect |
| 26. #10620281 | C22 | semidirect |
| 27. #10620279 | C22 | semidirect |
| 28. C4×Dic41 | C22 | semidirect |
| 48. C4×D41 | D4 | semidirect |
| 72. C41 | #535 | semidirect |
| 76. #127 | D41 | semidirect |
| 91. C2×D4 | C2×D41 | semidirect |
| 92. C2×D4 | C2×D41 | semidirect |
| 100. C42 | C2×D41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10620308 | 2 |
| C2×D4×D41 | 2 |
| #13050160 | 2 |
| #13050152 | 2 |
| #13050151 | 2 |
| #13050136 | 2 |
| #13050132 | 2 |
| #13050121 | 2 |
| #127×C41 | 2 |
| #535 | 41 |