Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
370 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 370 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. #27133266 | C2 | semidirect |
| 2. #27132965 | C2 | semidirect |
| 3. #27132962 | C2 | semidirect |
| 4. #27132916 | C2 | semidirect |
| 5. #27132897 | C2 | semidirect |
| 6. #27132857 | C2 | semidirect |
| 7. #27132856 | C2 | semidirect |
| 8. #27132691 | C2 | semidirect |
| 9. #469×C191 | C2 | semidirect |
| 109. C191 | #3259 | semidirect |
| 115. #469 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133266 | 2 |
| #27132965 | 2 |
| #27132962 | 2 |
| #27132916 | 2 |
| #27132897 | 2 |
| #27132857 | 2 |
| #27132856 | 2 |
| #27132691 | 2 |
| #469×C191 | 2 |
| #3259 | 191 |