Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
522 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×#63627 | C2 | semidirect |
| 2. C4×#3746 | C2 | semidirect |
| 4. C32×C4⋊C16 | C2 | semidirect |
| 5. #10589375 | C2 | semidirect |
| 20. C3×C4⋊C16 | D3 | semidirect |
| 33. #3746 | D4 | semidirect |
| 67. C4⋊C16 | C3⋊D3 | semidirect |
| 90. C32×C4 | SD32 | semidirect |
| 145. C3×C4 | #800 | semidirect |
| 150. C32 | #2207 | semidirect |
| 177. C4 | #63627 | semidirect |
| 180. C3 | #69292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63627 | 2 |
| C4×#3746 | 2 |
| #10592394 | 2 |
| C32×C4⋊C16 | 2 |
| #10589375 | 2 |
| #69292 | 3 |