Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
112 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 37 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. Q32×D23 | C2 | semidirect |
| 3. #13092256 | C2 | semidirect |
| 4. #13092255 | C2 | semidirect |
| 5. #13092254 | C2 | semidirect |
| 6. C32×D23 | C2 | semidirect |
| 7. C23×SD64 | C2 | semidirect |
| 10. C23×Q32 | C22 | semidirect |
| 14. Dic184 | C22 | semidirect |
| 17. C23×C32 | C22 | semidirect |
| 18. C23⋊C32 | C22 | semidirect |
| 55. SD64 | D23 | direct (N × H) |
| 60. D23 | SD64 | direct (N × H) |
| 65. Q32 | C2×D23 | semidirect |
| 71. C32 | C2×D23 | semidirect |
| 72. C23 | C2×SD64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q32×D23 | 2 |
| D16×D23 | 2 |
| #13092256 | 2 |
| #13092255 | 2 |
| #13092254 | 2 |
| C32×D23 | 2 |
| C23×SD64 | 2 |
| C2×SD64 | 23 |