Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27133220 | C2 | semidirect |
| 3. #27133005 | C2 | semidirect |
| 4. #27132959 | C2 | semidirect |
| 5. #27132954 | C2 | semidirect |
| 6. #27132874 | C2 | semidirect |
| 7. #27132869 | C2 | semidirect |
| 9. #27132771 | C2 | semidirect |
| 10. #27132765 | C2 | semidirect |
| 11. #432×C191 | C2 | semidirect |
| 136. C191 | #3116 | semidirect |
| 148. #432 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133220 | 2 |
| C4×#15690287 | 2 |
| #27133005 | 2 |
| #27132959 | 2 |
| #27132954 | 2 |
| #27132874 | 2 |
| #27132869 | 2 |
| #27132827 | 2 |
| #27132771 | 2 |
| #27132765 | 2 |
| #432×C191 | 2 |
| #3116 | 191 |