Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 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. #27133463 | C2 | semidirect |
| 2. C2×#20259344 | C2 | semidirect |
| 3. C2×#20259328 | C2 | semidirect |
| 4. #27132939 | C2 | semidirect |
| 5. #27132934 | C2 | semidirect |
| 6. #27132927 | C2 | semidirect |
| 7. #27132645 | C2 | semidirect |
| 8. C2×#108×C191 | C2 | semidirect |
| 20. C2×Dic764 | C22 | semidirect |
| 21. C2×#15690276 | C22 | semidirect |
| 22. C2×D1528 | C22 | semidirect |
| 30. #20259240 | C22 | semidirect |
| 31. #20259238 | C22 | semidirect |
| 34. #108×C191 | C22 | semidirect |
| 35. #108×C191 | C22 | semidirect |
| 132. C191 | #3067 | semidirect |
| 140. C2×#108 | D191 | semidirect |
| 165. #108 | C2×D191 | semidirect |
| 166. #108 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133463 | 2 |
| C2×#20259344 | 2 |
| C2×#20259328 | 2 |
| #27132939 | 2 |
| #27132934 | 2 |
| #27132927 | 2 |
| #27132645 | 2 |
| C2×#108×C191 | 2 |
| #3067 | 191 |