Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 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. #27133198 | C2 | semidirect |
| 2. #27133047 | C2 | semidirect |
| 3. #27133020 | C2 | semidirect |
| 4. #27132922 | C2 | semidirect |
| 6. #27132910 | C2 | semidirect |
| 7. #27132774 | C2 | semidirect |
| 8. #27132769 | C2 | semidirect |
| 9. #27132762 | C2 | semidirect |
| 10. C4×#15690270 | C2 | semidirect |
| 11. #499×C191 | C2 | semidirect |
| 109. C191 | #3183 | semidirect |
| 112. #499 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133198 | 2 |
| #27133047 | 2 |
| #27133020 | 2 |
| #27132922 | 2 |
| #27132917 | 2 |
| #27132910 | 2 |
| #27132774 | 2 |
| #27132769 | 2 |
| #27132762 | 2 |
| C4×#15690270 | 2 |
| #499×C191 | 2 |
| #3183 | 191 |