Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #27132949 | C2 | semidirect |
| 5. #27132948 | C2 | semidirect |
| 6. #27132870 | C2 | semidirect |
| 8. #27132770 | C2 | semidirect |
| 9. #27132767 | C2 | semidirect |
| 11. #462×C191 | C2 | semidirect |
| 132. C191 | #3113 | semidirect |
| 140. #462 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133218 | 2 |
| C4×Q8×D191 | 2 |
| #27132992 | 2 |
| #27132949 | 2 |
| #27132948 | 2 |
| #27132870 | 2 |
| #27132817 | 2 |
| #27132770 | 2 |
| #27132767 | 2 |
| #27132719 | 2 |
| #462×C191 | 2 |
| #3113 | 191 |