Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
330 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 111 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×D397 |
| commutator, socle, cosocle | C22×C397 | C24 |
| Fitting | #120×C397 | C2 |
| hypercenter | #120 | D397 |
| hypocenter | C397 | #525 |
| LCS | G ▷ C22×C397 ▷ C397 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20263730 | C2 | semidirect |
| 2. C23×Dic397 | C2 | semidirect |
| 3. #27163080 | C2 | semidirect |
| 4. #27163077 | C2 | semidirect |
| 5. #27163073 | C2 | semidirect |
| 6. #27163068 | C2 | semidirect |
| 7. #27163065 | C2 | semidirect |
| 8. D4×Dic397 | C2 | semidirect |
| 9. #27163056 | C2 | semidirect |
| 10. #27163052 | C2 | semidirect |
| 11. #120×C397 | C2 | semidirect |
| 13. C2×Dic794 | C22 | semidirect |
| 16. C2×C22⋊D397 | C22 | semidirect |
| 22. C22×Dic397 | C22 | semidirect |
| 23. C2×C4×D397 | C22 | semidirect |
| 24. C4⋊Dic397 | C22 | semidirect |
| 25. #20263710 | C22 | semidirect |
| 26. #20263710 | C22 | semidirect |
| 29. C22⋊Dic397 | C22 | semidirect |
| 30. #20263708 | C22 | semidirect |
| 31. C4×Dic397 | C22 | semidirect |
| 46. C2×Dic397 | D4 | semidirect |
| 69. C22×C397 | #41 | semidirect |
| 86. C397 | #525 | semidirect |
| 95. #120 | D397 | semidirect |
| 158. C22 | #20263730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263730 | 2 |
| C23×Dic397 | 2 |
| #27163080 | 2 |
| #27163077 | 2 |
| #27163073 | 2 |
| #27163068 | 2 |
| #27163065 | 2 |
| D4×Dic397 | 2 |
| #27163056 | 2 |
| #27163052 | 2 |
| #120×C397 | 2 |
| #525 | 397 |