Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
512 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 3. #13092453 | C2 | direct (N × H) |
| 4. C2×#10624989 | C2 | semidirect |
| 5. C2×#10624990 | C2 | semidirect |
| 18. C22×C23⋊C8 | C4 | semidirect |
| 22. #10624990 | C22 | semidirect |
| 23. #10624989 | C22 | semidirect |
| 43. C2×C23⋊C8 | C2×C4 | semidirect |
| 85. C2×C23 | #427 | semidirect |
| 105. C23 | C2×#427 | semidirect |
| 160. C2 | #13092453 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C23⋊C8 | 2 |
| C2×#10625097 | 2 |
| #13092453 | 2 |
| C2×#10624989 | 2 |
| C2×#10624990 | 2 |
| C2×C23×#117 | 2 |
| C2×#427 | 23 |