Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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. #27133036 | C2 | semidirect |
| 2. #27132943 | C2 | semidirect |
| 4. #27132414 | C2 | semidirect |
| 5. #27132410 | C2 | semidirect |
| 6. #27132406 | C2 | semidirect |
| 7. C8×D4×C191 | C2 | semidirect |
| 56. D4×C191 | SD16 | semidirect |
| 65. C8×C191 | D8 | semidirect |
| 85. C191 | #1665 | semidirect |
| 90. C8×D4 | D191 | semidirect |
| 139. D4 | #15690276 | semidirect |
| 151. C8 | #15690272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133036 | 2 |
| #27132943 | 2 |
| #27132858 | 2 |
| #27132414 | 2 |
| #27132410 | 2 |
| #27132406 | 2 |
| C8×D4×C191 | 2 |
| #1665 | 191 |