Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
166 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 55 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. #27133068 | C2 | semidirect |
| 4. #27132410 | C2 | semidirect |
| 5. #334×C191 | C2 | semidirect |
| 45. C8×C191 | SD16 | semidirect |
| 60. C191 | #1693 | semidirect |
| 65. #334 | D191 | semidirect |
| 106. C8 | #15690276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133068 | 2 |
| #27132869 | 2 |
| #27132742 | 2 |
| #27132410 | 2 |
| #334×C191 | 2 |
| #1693 | 191 |