Finite Group DatabasebetaFinite Group DatabasebetaOrder 4608.
924 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 205 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. #72254956 | C2 | semidirect |
| 2. #72254915 | C2 | semidirect |
| 4. C32×#7463 | C2 | semidirect |
| 5. #72245317 | C2 | semidirect |
| 21. C3×#7463 | D3 | semidirect |
| 35. #10589314 | C8 | semidirect |
| 60. #63626 | C2×C8 | semidirect |
| 62. C32×C32 | C2×C8 | semidirect |
| 66. #7463 | C3⋊D3 | semidirect |
| 124. C3×C32 | D3×C8 | semidirect |
| 193. C32 | C8×C3⋊D3 | semidirect |
| 234. C32 | #151085 | semidirect |
| 259. C3 | #72245028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72254956 | 2 |
| #72254915 | 2 |
| #72254882 | 2 |
| C32×#7463 | 2 |
| #72245317 | 2 |
| #72245028 | 3 |