Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
438 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 3. C2×#63372 | C2 | semidirect |
| 4. #10588227 | C2 | semidirect |
| 81. C22×C9 | #108 | semidirect |
| 142. C9 | #1810 | semidirect |
| 167. C22 | #63372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C8×C9 | 2 |
| #10588887 | 2 |
| C2×#63372 | 2 |
| #10588227 | 2 |
| #71977 | 3 |