Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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. #27133220 | C2 | semidirect |
| 3. #27133036 | C2 | semidirect |
| 4. #27133010 | C2 | semidirect |
| 5. #27132864 | C2 | semidirect |
| 6. #27132816 | C2 | semidirect |
| 7. #431×C191 | C2 | semidirect |
| 11. C2×#15690276 | C22 | semidirect |
| 12. #20259322 | C22 | semidirect |
| 13. #20259322 | C22 | semidirect |
| 22. C4×Dic382 | C22 | semidirect |
| 24. #20259244 | C22 | semidirect |
| 26. C4⋊C8×C191 | C22 | semidirect |
| 28. C4×C8×C191 | C22 | semidirect |
| 75. C2×C4×C191 | SD16 | semidirect |
| 104. C191 | #3208 | semidirect |
| 112. #431 | D191 | semidirect |
| 130. C4⋊C8 | C2×D191 | semidirect |
| 133. C4×C8 | C2×D191 | semidirect |
| 180. C2×C4 | #15690276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133220 | 2 |
| C2×#20259319 | 2 |
| #27133036 | 2 |
| #27133010 | 2 |
| #27132864 | 2 |
| #27132816 | 2 |
| #431×C191 | 2 |
| #3208 | 191 |