Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
438 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 438 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. #27133211 | C2 | semidirect |
| 2. #27133211 | C2 | semidirect |
| 3. #27133035 | C2 | semidirect |
| 4. #27133014 | C2 | semidirect |
| 5. #27133009 | C2 | semidirect |
| 6. #27132876 | C2 | semidirect |
| 7. #27132805 | C2 | semidirect |
| 8. #27132714 | C2 | semidirect |
| 9. #493×C191 | C2 | semidirect |
| 120. C191 | #3207 | semidirect |
| 124. #493 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133211 | 2 |
| #27133035 | 2 |
| #27133014 | 2 |
| #27133009 | 2 |
| #27132876 | 2 |
| #27132805 | 2 |
| #27132714 | 2 |
| #493×C191 | 2 |
| #3207 | 191 |