Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
828 conjugacy classes of subgroups; only the 262 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 262 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 |
|---|---|---|
| 4. #10588765 | C2 | direct (N × H) |
| 61. C2×C4×C9 | Q16 | semidirect |
| 98. C4×C9 | C2×Q16 | semidirect |
| 129. C2×C9 | #494 | semidirect |
| 157. C9 | C2×#494 | semidirect |
| 167. C2×C4 | #3674 | semidirect |
| 182. C4 | C2×#3674 | semidirect |
| 185. C2 | #10588765 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×C4⋊Q8 | 2 |
| C22×#3674 | 2 |
| C2×#63431 | 2 |
| #10588765 | 2 |
| C2×C4×C9⋊C8 | 2 |
| C2×#5092 | 3 |