Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
214 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 97 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×D389 |
| commutator, socle, cosocle | C22×C389 | C24 |
| Fitting | #117×C389 | C2 |
| prime radical | C2×C22⋊D389 | C22 |
| hypercenter | #117 | D389 |
| hypocenter | C389 | #552 |
| LCS | G ▷ C22×C389 ▷ C389 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27159379 | C2 | semidirect |
| 2. #27159378 | C2 | semidirect |
| 3. #27159376 | C2 | semidirect |
| 4. #27159374 | C2 | semidirect |
| 5. #27159374 | C2 | semidirect |
| 8. #27159362 | C2 | semidirect |
| 9. #27159361 | C2 | semidirect |
| 10. C4×Dic778 | C2 | semidirect |
| 12. #27159341 | C2 | semidirect |
| 13. #27159340 | C2 | semidirect |
| 14. C2×#20261945 | C2 | semidirect |
| 15. #117×C389 | C2 | semidirect |
| 97. C389 | #552 | semidirect |
| 112. #117 | D389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27159379 | 2 |
| #27159378 | 2 |
| #27159376 | 2 |
| #27159374 | 2 |
| #27159368 | 2 |
| #27159367 | 2 |
| #27159362 | 2 |
| #27159361 | 2 |
| C4×Dic778 | 2 |
| #27159344 | 2 |
| #27159341 | 2 |
| #27159340 | 2 |
| C2×#20261945 | 2 |
| #117×C389 | 2 |
| #552 | 389 |