Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #27132679 | C2 | semidirect |
| 3. #27132637 | C2 | semidirect |
| 4. #27132424 | C2 | semidirect |
| 5. #568×C191 | C2 | semidirect |
| 7. #20259320 | C4 | semidirect |
| 8. #20259318 | C4 | semidirect |
| 9. #20259311 | C4 | semidirect |
| 10. #20259309 | C4 | semidirect |
| 47. M16×C191 | D4 | semidirect |
| 95. C191 | #1884 | semidirect |
| 97. #568 | D191 | semidirect |
| 134. M16 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133209 | 2 |
| #27132679 | 2 |
| #27132637 | 2 |
| #27132424 | 2 |
| #568×C191 | 2 |
| #1884 | 191 |