Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
540 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 217 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. #13092324 | C2 | semidirect |
| 2. #13092310 | C2 | semidirect |
| 3. #13092310 | C2 | semidirect |
| 5. #13092292 | C2 | semidirect |
| 6. #13092285 | C2 | semidirect |
| 7. C4×C4⋊Dic23 | C2 | semidirect |
| 8. C22⋊C4×Dic23 | C2 | semidirect |
| 13. C23×#124 | C4 | semidirect |
| 34. C2×Q8×C23 | C2×C4 | semidirect |
| 48. C22⋊C4×C23 | C2×C4 | semidirect |
| 49. C22⋊C4×C23 | C2×C4 | semidirect |
| 50. C42×C23 | C2×C4 | semidirect |
| 131. #124 | Dic23 | semidirect |
| 150. C23 | #2337 | semidirect |
| 153. C2×Q8 | C2×Dic23 | semidirect |
| 172. C22⋊C4 | C2×Dic23 | semidirect |
| 173. C22⋊C4 | C2×Dic23 | semidirect |
| 177. C42 | C2×Dic23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13092324 | 2 |
| #13092310 | 2 |
| #13092297 | 2 |
| #13092292 | 2 |
| #13092285 | 2 |
| C4×C4⋊Dic23 | 2 |
| C22⋊C4×Dic23 | 2 |
| C2×C23×#124 | 2 |
| #2337 | 23 |