Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
720 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 246 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. #10588533 | C2 | direct (N × H) |
| 15. C2×Dic36 | C4 | semidirect |
| 46. Dic36 | C2×C4 | semidirect |
| 142. C2×C9 | #441 | semidirect |
| 173. C9 | C2×#441 | semidirect |
| 203. C2 | #10588533 | 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×#63449 | 2 |
| C2×C9×#106 | 2 |
| C2×#63375 | 2 |
| C2×#63368 | 2 |
| #10588533 | 2 |
| C2×#4853 | 3 |