Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1033 conjugacy classes of subgroups; only the 276 normal subgroups are shown.
This group has 1033 conjugacy classes of subgroups — too many to draw. Only its 276 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 |
|---|---|---|
| 6. #10590791 | C2 | direct (N × H) |
| 17. C2×#3718 | C4 | semidirect |
| 49. #3718 | C2×C4 | semidirect |
| 193. C2×C32 | #441 | semidirect |
| 235. C32 | C2×#441 | semidirect |
| 255. C2×C3 | #4789 | semidirect |
| 269. C3 | C2×#4789 | semidirect |
| 270. C2 | #10590791 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63843 | 2 |
| C22×#3718 | 2 |
| C2×#63642 | 2 |
| C2×C3×#816 | 2 |
| C2×#63574 | 2 |
| #10590791 | 2 |
| C2×#4789 | 3 |