Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 498 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. C32×#494 | C2 | semidirect |
| 4. #10589430 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 17. C3×#494 | D3 | semidirect |
| 64. #494 | C3⋊D3 | semidirect |
| 90. C32×C4 | SD32 | semidirect |
| 144. C3×C4 | #828 | semidirect |
| 148. C32 | #2208 | semidirect |
| 174. C4 | #63655 | semidirect |
| 177. C3 | #71315 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#494 | 2 |
| C2×#63655 | 2 |
| C4×#3745 | 2 |
| #10589430 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| #71315 | 3 |