Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
576 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 198 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. #10588746 | C2 | direct (N × H) |
| 118. C2×C9 | #491 | semidirect |
| 144. C9 | C2×#491 | semidirect |
| 170. C2 | #10588746 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#125 | 2 |
| C2×#63431 | 2 |
| #10588746 | 2 |
| C2×#63368 | 2 |
| C2×#63362 | 2 |
| C2×#5069 | 3 |