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. #27133268 | C2 | semidirect |
| 2. #27132963 | C2 | semidirect |
| 3. #27132960 | C2 | semidirect |
| 4. #27132914 | C2 | semidirect |
| 5. #27132897 | C2 | semidirect |
| 6. #27132858 | C2 | semidirect |
| 7. #27132855 | C2 | semidirect |
| 8. #27132690 | C2 | semidirect |
| 9. #540×C191 | C2 | semidirect |
| 106. C191 | #3259 | semidirect |
| 109. #540 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133268 | 2 |
| #27132963 | 2 |
| #27132960 | 2 |
| #27132914 | 2 |
| #27132897 | 2 |
| #27132858 | 2 |
| #27132855 | 2 |
| #27132690 | 2 |
| #540×C191 | 2 |
| #3259 | 191 |