Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
338 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #27133062 | C2 | semidirect |
| 4. #27133042 | C2 | semidirect |
| 5. #27133032 | C2 | semidirect |
| 8. #27132767 | C2 | semidirect |
| 9. #27132755 | C2 | semidirect |
| 11. #491×C191 | C2 | semidirect |
| 102. C191 | #3177 | semidirect |
| 109. #491 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133276 | 2 |
| #27133274 | 2 |
| #27133062 | 2 |
| #27133042 | 2 |
| #27133032 | 2 |
| #27132920 | 2 |
| #27132903 | 2 |
| #27132767 | 2 |
| #27132755 | 2 |
| #27132620 | 2 |
| #491×C191 | 2 |
| #3177 | 191 |