Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
828 conjugacy classes of subgroups; only the 294 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 294 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. #10588365 | C2 | direct (N × H) |
| 42. C2×C4×C9 | Q16 | semidirect |
| 72. C4×C9 | C2×Q16 | semidirect |
| 95. C2×C9 | #494 | semidirect |
| 117. C9 | C2×#494 | semidirect |
| 123. C2×C4 | Dic36 | semidirect |
| 137. C4 | C2×Dic36 | semidirect |
| 140. C2 | #10588365 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic36 | 2 |
| C2×#63431 | 2 |
| C2×C4×C8×C9 | 2 |
| #10588365 | 2 |
| C2×#4699 | 3 |