Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #27133294 | C2 | semidirect |
| 3. #27132972 | C2 | semidirect |
| 4. #27132961 | C2 | semidirect |
| 5. #27132951 | C2 | semidirect |
| 6. #27132946 | C2 | semidirect |
| 7. #27132705 | C2 | semidirect |
| 8. C2×#20259253 | C2 | semidirect |
| 9. #27132691 | C2 | semidirect |
| 64. #41×C191 | Q8 | semidirect |
| 123. C191 | #3084 | semidirect |
| 166. #41 | Dic382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133294 | 2 |
| #27133146 | 2 |
| #27132972 | 2 |
| #27132961 | 2 |
| #27132951 | 2 |
| #27132946 | 2 |
| #27132705 | 2 |
| C2×#20259253 | 2 |
| #27132691 | 2 |
| #27132659 | 2 |
| #417×C191 | 2 |
| #3084 | 191 |