Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
432 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 145 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. C23×C23⋊C8 | C2 | semidirect |
| 2. C2×C22⋊(C23⋊C8) | C2 | semidirect |
| 3. C2×C22⋊(C23⋊C8) | C2 | semidirect |
| 4. #13092172 | C2 | semidirect |
| 25. C2×D4×C23 | C8 | semidirect |
| 50. C2×C23⋊C8 | D4 | semidirect |
| 59. C23×C23 | C2×C8 | semidirect |
| 77. C2×C4×C23 | C2×C8 | semidirect |
| 94. C22×C23 | C22⋊C8 | semidirect |
| 134. C23 | #1869 | semidirect |
| 139. C2×D4 | C23⋊C8 | semidirect |
| 172. C23 | C2×C23⋊C8 | semidirect |
| 190. C2×C4 | C2×C23⋊C8 | semidirect |
| 207. C22 | C22⋊(C23⋊C8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C23⋊C8 | 2 |
| C2×C22⋊(C23⋊C8) | 2 |
| #13092172 | 2 |
| C2×C4×D4×C23 | 2 |
| #1869 | 23 |