Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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. #13092820 | C2 | semidirect |
| 3. #13092791 | C2 | semidirect |
| 4. #13092789 | C2 | semidirect |
| 5. #13092764 | C2 | semidirect |
| 6. C8×C23⋊C8 | C2 | semidirect |
| 7. C23×#486 | C2 | semidirect |
| 56. C23⋊C8 | D8 | semidirect |
| 57. C23⋊C8 | SD16 | semidirect |
| 76. #486 | D23 | semidirect |
| 96. C23 | #1706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13092820 | 2 |
| #13092793 | 2 |
| #13092791 | 2 |
| #13092789 | 2 |
| #13092764 | 2 |
| C8×C23⋊C8 | 2 |
| C23×#486 | 2 |
| #1706 | 23 |