Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
730 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 3. #10590053 | C2 | direct (N × H) |
| 11. C2×#3712 | C4 | semidirect |
| 14. #63818 | C4 | semidirect |
| 39. #3712 | C2×C4 | semidirect |
| 186. C2×C32 | #343 | semidirect |
| 190. C3⋊D3 | #343 | semidirect |
| 242. C32 | C2×#343 | semidirect |
| 312. C2 | #10590053 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#157 | 2 |
| C2×#63818 | 2 |
| #10590053 | 2 |
| C2×#343 | 9 |