Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 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. #27159431 | C2 | semidirect |
| 2. #27159414 | C2 | semidirect |
| 3. #27159413 | C2 | semidirect |
| 4. #27159403 | C2 | semidirect |
| 5. C2×Dic1556 | C2 | semidirect |
| 6. Q16×D389 | C2 | semidirect |
| 7. #27159390 | C2 | semidirect |
| 8. #135×C389 | C2 | semidirect |
| 59. C389 | #578 | semidirect |
| 65. #135 | D389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27159431 | 2 |
| #27159414 | 2 |
| #27159413 | 2 |
| #27159403 | 2 |
| C2×Dic1556 | 2 |
| Q16×D389 | 2 |
| #27159390 | 2 |
| #135×C389 | 2 |
| #578 | 389 |