Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 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. #27132705 | C2 | semidirect |
| 5. #27132528 | C2 | semidirect |
| 6. #27132424 | C2 | semidirect |
| 7. #343×C191 | C2 | semidirect |
| 19. #20259248 | C4 | semidirect |
| 47. C4×Dic191 | C2×C4 | semidirect |
| 53. M16×C191 | C2×C4 | semidirect |
| 111. C191 | #1860 | semidirect |
| 118. #343 | D191 | semidirect |
| 154. M16 | C4×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133144 | 2 |
| #27132705 | 2 |
| C2×#20259248 | 2 |
| #27132665 | 2 |
| #27132528 | 2 |
| #27132424 | 2 |
| #343×C191 | 2 |
| #1860 | 191 |