Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4×Q8×D191 | C2 | semidirect |
| 3. #27132975 | C2 | semidirect |
| 4. #27132959 | C2 | semidirect |
| 5. #27132958 | C2 | semidirect |
| 6. #27132860 | C2 | semidirect |
| 7. #27132800 | C2 | semidirect |
| 8. #27132764 | C2 | semidirect |
| 9. #27132760 | C2 | semidirect |
| 10. #27132719 | C2 | semidirect |
| 11. #460×C191 | C2 | semidirect |
| 87. Dic382 | #41 | semidirect |
| 105. Q8×C191 | #41 | semidirect |
| 140. C191 | #3112 | semidirect |
| 148. #460 | D191 | semidirect |
| 231. 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×Q8×D191 | 2 |
| #27132975 | 2 |
| #27132959 | 2 |
| #27132958 | 2 |
| #27132860 | 2 |
| #27132800 | 2 |
| #27132764 | 2 |
| #27132760 | 2 |
| #27132719 | 2 |
| #460×C191 | 2 |
| #3112 | 191 |