Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 95 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 | C4×Q8×C389 | C2 |
| prime radical | #27159359 | C2 |
| hypercenter | C4×Q8 | D389 |
| hypocenter | C389 | #542 |
| LCS | G ▷ C22×C389 ▷ C389 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27159383 | C2 | semidirect |
| 2. #27159378 | C2 | semidirect |
| 3. #27159373 | C2 | semidirect |
| 4. #27159372 | C2 | semidirect |
| 5. #27159369 | C2 | semidirect |
| 6. #27159362 | C2 | semidirect |
| 7. #27159360 | C2 | semidirect |
| 9. C4×D1556 | C2 | semidirect |
| 10. #27159341 | C2 | semidirect |
| 11. C4×Q8×C389 | C2 | semidirect |
| 73. C389 | #542 | semidirect |
| 83. C4×Q8 | D389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27159383 | 2 |
| #27159378 | 2 |
| #27159373 | 2 |
| #27159372 | 2 |
| #27159369 | 2 |
| #27159362 | 2 |
| #27159360 | 2 |
| #27159359 | 2 |
| C4×D1556 | 2 |
| #27159341 | 2 |
| C4×Q8×C389 | 2 |
| #542 | 389 |