Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
437 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 437 conjugacy classes of subgroups — too many to draw. Only its 89 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. #10589488 | C2 | direct (N × H) |
| 20. C2×Q8⋊C9 | Q8 | semidirect |
| 44. Q8⋊C9 | C2×Q8 | semidirect |
| 117. C2×Q8 | Dic18 | semidirect |
| 148. Q8 | C2×Dic18 | semidirect |
| 175. C2 | #10589488 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Q8⋊C9 | 2 |
| C2×#63421 | 2 |
| #10589488 | 2 |
| C2×#5020 | 3 |
| C22×Dic18 | 4 |