Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #27133211 | C2 | semidirect |
| 2. C4×#15690288 | C2 | semidirect |
| 3. #27132985 | C2 | semidirect |
| 4. #27132948 | C2 | semidirect |
| 5. #27132944 | C2 | semidirect |
| 6. #27132855 | C2 | semidirect |
| 7. #27132807 | C2 | semidirect |
| 8. #27132772 | C2 | semidirect |
| 9. #27132764 | C2 | semidirect |
| 10. #27132719 | C2 | semidirect |
| 11. #460×C191 | C2 | semidirect |
| 88. D764 | #41 | semidirect |
| 106. Q8×C191 | #41 | semidirect |
| 144. C191 | #3115 | semidirect |
| 151. #460 | D191 | semidirect |
| 233. Q8 | #15690286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133211 | 2 |
| C4×#15690288 | 2 |
| #27132985 | 2 |
| #27132948 | 2 |
| #27132944 | 2 |
| #27132855 | 2 |
| #27132807 | 2 |
| #27132772 | 2 |
| #27132764 | 2 |
| #27132719 | 2 |
| #460×C191 | 2 |
| #3115 | 191 |