Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27159379 | C2 | semidirect |
| 2. #27159375 | C2 | semidirect |
| 3. #27159374 | C2 | semidirect |
| 5. #27159364 | C2 | semidirect |
| 6. #27159363 | C2 | semidirect |
| 7. #27159349 | C2 | semidirect |
| 9. #27159343 | C2 | semidirect |
| 10. #27159342 | C2 | semidirect |
| 11. C2×C4⋊C4×C389 | C2 | semidirect |
| 72. C389 | #552 | semidirect |
| 84. C2×C4⋊C4 | D389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27159379 | 2 |
| #27159375 | 2 |
| #27159374 | 2 |
| #27159367 | 2 |
| #27159364 | 2 |
| #27159363 | 2 |
| #27159349 | 2 |
| C4×C22⋊D389 | 2 |
| #27159343 | 2 |
| #27159342 | 2 |
| C2×C4⋊C4×C389 | 2 |
| #552 | 389 |