Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
280 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 4. #13092149 | C2 | semidirect |
| 5. Q8⋊(C23⋊C8) | C2 | semidirect |
| 6. #13092147 | C2 | semidirect |
| 7. C23×Q8⋊C8 | C2 | semidirect |
| 29. Q8×D23 | C8 | semidirect |
| 60. Q8×C23 | C2×C8 | semidirect |
| 80. Dic46 | C2×C8 | semidirect |
| 108. Q8⋊C8 | D23 | direct (N × H) |
| 112. D23 | Q8⋊C8 | direct (N × H) |
| 132. C23 | C2×Q8⋊C8 | semidirect |
| 169. Q8 | C8×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D23 | 2 |
| C4⋊C8×D23 | 2 |
| C4×C8×D23 | 2 |
| #13092149 | 2 |
| Q8⋊(C23⋊C8) | 2 |
| #13092147 | 2 |
| C23×Q8⋊C8 | 2 |
| C2×Q8⋊C8 | 23 |