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 |
|---|---|---|
| 2. C2×#63654 | C2 | semidirect |
| 3. C4×#3746 | C2 | semidirect |
| 4. #10589428 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 36. #3746 | D4 | semidirect |
| 90. C32×C4 | SD32 | semidirect |
| 145. C3×C4 | #827 | semidirect |
| 150. C32 | #2207 | semidirect |
| 177. C4 | #63654 | semidirect |
| 180. C3 | #71294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#493 | 2 |
| C2×#63654 | 2 |
| C4×#3746 | 2 |
| #10589428 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| #71294 | 3 |