Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
237 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 237 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 1. C2×Dic72 | C2 | semidirect |
| 4. C4×Dic36 | C2 | semidirect |
| 5. C9×C4⋊C16 | C2 | semidirect |
| 7. #10588180 | C2 | semidirect |
| 83. C4⋊C16 | D9 | semidirect |
| 181. C9 | #2211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic72 | 2 |
| C2×#63359 | 2 |
| #10588378 | 2 |
| C4×Dic36 | 2 |
| C9×C4⋊C16 | 2 |
| #10588186 | 2 |
| #10588180 | 2 |
| #69294 | 3 |