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. #27159432 | C2 | semidirect |
| 2. #27159431 | C2 | semidirect |
| 3. #27159417 | C2 | semidirect |
| 4. #27159416 | C2 | semidirect |
| 5. #27159413 | C2 | semidirect |
| 6. #27159405 | C2 | semidirect |
| 7. #27159404 | C2 | semidirect |
| 8. C2×#20261956 | C2 | semidirect |
| 9. Q16×D389 | C2 | semidirect |
| 10. #27159392 | C2 | semidirect |
| 11. #137×C389 | C2 | semidirect |
| 87. C389 | #578 | semidirect |
| 94. #137 | D389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27159432 | 2 |
| #27159431 | 2 |
| #27159417 | 2 |
| #27159416 | 2 |
| #27159413 | 2 |
| #27159405 | 2 |
| #27159404 | 2 |
| C2×#20261956 | 2 |
| Q16×D389 | 2 |
| #27159392 | 2 |
| #137×C389 | 2 |
| #578 | 389 |