Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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. #27133242 | C2 | semidirect |
| 2. #27133000 | C2 | semidirect |
| 3. #27132975 | C2 | semidirect |
| 4. #27132907 | C2 | semidirect |
| 5. #27132904 | C2 | semidirect |
| 6. #27132826 | C2 | semidirect |
| 7. #27132805 | C2 | semidirect |
| 8. #27132629 | C2 | semidirect |
| 9. #466×C191 | C2 | semidirect |
| 119. C191 | #3203 | semidirect |
| 126. #466 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133242 | 2 |
| #27133000 | 2 |
| #27132975 | 2 |
| #27132907 | 2 |
| #27132904 | 2 |
| #27132826 | 2 |
| #27132805 | 2 |
| #27132629 | 2 |
| #466×C191 | 2 |
| #3203 | 191 |