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×#20261953 | C2 | semidirect |
| 3. C4×D1556 | C2 | semidirect |
| 4. C4⋊#15691005 | C2 | semidirect |
| 5. #27159308 | C2 | semidirect |
| 6. #27159305 | C2 | semidirect |
| 7. #124×C389 | C2 | semidirect |
| 55. C389 | #463 | semidirect |
| 59. #124 | D389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20261953 | 2 |
| C2×#20261951 | 2 |
| C4×D1556 | 2 |
| C4⋊#15691005 | 2 |
| #27159308 | 2 |
| #27159305 | 2 |
| #124×C389 | 2 |
| #463 | 389 |