Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27133282 | C2 | semidirect |
| 2. #27133061 | C2 | semidirect |
| 3. #27133022 | C2 | semidirect |
| 4. #27132918 | C2 | semidirect |
| 6. #27132889 | C2 | semidirect |
| 7. #27132775 | C2 | semidirect |
| 8. #27132770 | C2 | semidirect |
| 9. SD16×Dic191 | C2 | semidirect |
| 10. #27132617 | C2 | semidirect |
| 11. #495×C191 | C2 | semidirect |
| 109. C191 | #3173 | semidirect |
| 113. #495 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133282 | 2 |
| #27133061 | 2 |
| #27133022 | 2 |
| #27132918 | 2 |
| #27132913 | 2 |
| #27132889 | 2 |
| #27132775 | 2 |
| #27132770 | 2 |
| SD16×Dic191 | 2 |
| #27132617 | 2 |
| #495×C191 | 2 |
| #3173 | 191 |