Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 172 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 |
|---|---|---|
| 2. #27132948 | C2 | semidirect |
| 4. #27132414 | C2 | semidirect |
| 5. #27132410 | C2 | semidirect |
| 7. C8×Q8×C191 | C2 | semidirect |
| 54. Q8×C191 | SD16 | semidirect |
| 62. C8×C191 | SD16 | semidirect |
| 79. C191 | #1666 | semidirect |
| 84. C8×Q8 | D191 | semidirect |
| 126. Q8 | #15690276 | semidirect |
| 142. C8 | #15690274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133036 | 2 |
| #27132948 | 2 |
| #27132863 | 2 |
| #27132414 | 2 |
| #27132410 | 2 |
| #27132406 | 2 |
| C8×Q8×C191 | 2 |
| #1666 | 191 |