Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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. C2×#20261955 | C2 | semidirect |
| 3. #27159372 | C2 | semidirect |
| 4. C4×D1556 | C2 | semidirect |
| 5. #27159309 | C2 | semidirect |
| 6. #27159306 | C2 | semidirect |
| 7. C4⋊C8×C389 | C2 | semidirect |
| 55. C389 | #463 | semidirect |
| 61. C4⋊C8 | D389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20261955 | 2 |
| C2×D3112 | 2 |
| #27159372 | 2 |
| C4×D1556 | 2 |
| #27159309 | 2 |
| #27159306 | 2 |
| C4⋊C8×C389 | 2 |
| #463 | 389 |