Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 2. C4×Dic778 | C2 | semidirect |
| 3. #27159317 | C2 | semidirect |
| 4. #27159307 | C2 | semidirect |
| 6. #27159295 | C2 | semidirect |
| 9. #20261954 | C4 | semidirect |
| 21. Dic778 | C2×C4 | semidirect |
| 25. #15691005 | C2×C4 | semidirect |
| 49. C389 | #440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20261954 | 2 |
| C4×Dic778 | 2 |
| #27159317 | 2 |
| #27159307 | 2 |
| #27159305 | 2 |
| #27159295 | 2 |
| C4×D4×C389 | 2 |
| #440 | 389 |