Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
250 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 61 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. #13092763 | C2 | semidirect |
| 2. #13092702 | C2 | semidirect |
| 3. #13092622 | C2 | semidirect |
| 4. #13092161 | C2 | semidirect |
| 5. Q8⋊(C23⋊C8) | C2 | semidirect |
| 6. D4⋊(C23⋊C8) | C2 | semidirect |
| 53. Q8×C23 | SD16 | semidirect |
| 124. C23 | #1642 | semidirect |
| 155. Q8 | #67273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13092763 | 2 |
| #13092702 | 2 |
| #13092622 | 2 |
| #13092161 | 2 |
| Q8⋊(C23⋊C8) | 2 |
| D4⋊(C23⋊C8) | 2 |
| C23×#550 | 2 |
| #1642 | 23 |