Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #27133141 | C2 | semidirect |
| 4. #27132766 | C2 | semidirect |
| 5. #27132748 | C2 | semidirect |
| 6. #27132699 | C2 | semidirect |
| 8. #27132621 | C2 | semidirect |
| 9. #419×C191 | C2 | semidirect |
| 11. C2×#15690274 | C4 | semidirect |
| 16. Q8×Dic191 | C22 | semidirect |
| 23. #20259255 | C22 | semidirect |
| 24. #20259253 | C22 | semidirect |
| 26. #20259232 | C22 | semidirect |
| 27. C8×Dic191 | C22 | semidirect |
| 31. #103×C191 | C22 | semidirect |
| 38. #15690274 | C2×C4 | semidirect |
| 39. #15690274 | C2×C4 | semidirect |
| 40. C2×C191⋊C8 | C2×C4 | semidirect |
| 54. C2×Q8×C191 | C2×C4 | semidirect |
| 103. C191 | #2949 | semidirect |
| 111. #419 | D191 | semidirect |
| 132. #103 | C2×D191 | semidirect |
| 139. C2×Q8 | C4×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690274 | 2 |
| #27133141 | 2 |
| #27133137 | 2 |
| #27132766 | 2 |
| #27132748 | 2 |
| #27132699 | 2 |
| #27132669 | 2 |
| #27132621 | 2 |
| #419×C191 | 2 |
| #2949 | 191 |