Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
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×D23 | C2 | semidirect |
| 3. #13092710 | C2 | semidirect |
| 4. #13092706 | C2 | semidirect |
| 5. #13092702 | C2 | semidirect |
| 6. #13092698 | C2 | semidirect |
| 7. #13092694 | C2 | semidirect |
| 8. #13092456 | C2 | semidirect |
| 9. #13092439 | C2 | semidirect |
| 11. C23×#475 | C2 | semidirect |
| 46. #67292 | Q8 | semidirect |
| 86. Q8×C23 | C2×Q8 | semidirect |
| 100. D92 | C2×Q8 | semidirect |
| 138. #475 | D23 | semidirect |
| 180. C23 | #3079 | semidirect |
| 226. Q8 | Q8×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D23 | 2 |
| C4×#67292 | 2 |
| #13092710 | 2 |
| #13092706 | 2 |
| #13092702 | 2 |
| #13092698 | 2 |
| #13092694 | 2 |
| #13092456 | 2 |
| #13092439 | 2 |
| #13092417 | 2 |
| C23×#475 | 2 |
| #3079 | 23 |