Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D191 | C2 | semidirect |
| 3. #27132957 | C2 | semidirect |
| 4. #27132951 | C2 | semidirect |
| 5. #27132949 | C2 | semidirect |
| 6. #27132945 | C2 | semidirect |
| 7. #27132943 | C2 | semidirect |
| 8. #27132704 | C2 | semidirect |
| 9. #27132685 | C2 | semidirect |
| 11. #474×C191 | C2 | semidirect |
| 44. #15690286 | Q8 | semidirect |
| 86. Dic382 | C2×Q8 | semidirect |
| 105. D4×C191 | C2×Q8 | semidirect |
| 137. C191 | #3079 | semidirect |
| 146. #474 | D191 | semidirect |
| 229. D4 | Q8×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D191 | 2 |
| C4×#15690286 | 2 |
| #27132957 | 2 |
| #27132951 | 2 |
| #27132949 | 2 |
| #27132945 | 2 |
| #27132943 | 2 |
| #27132704 | 2 |
| #27132685 | 2 |
| #27132661 | 2 |
| #474×C191 | 2 |
| #3079 | 191 |