Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2436 conjugacy classes of subgroups; only the 894 normal subgroups are shown.
This group has 2436 conjugacy classes of subgroups — too many to draw. Only its 894 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×#63506 | C2 | direct (N × H) |
| 15. #63506 | C22 | direct (N × H) |
| 31. C22×Dic9 | Q8 | semidirect |
| 59. C2×Dic9 | C2×Q8 | semidirect |
| 83. C22×C9 | C4⋊Q8 | semidirect |
| 90. Dic9 | C22×Q8 | semidirect |
| 115. C2×C9 | C2×C4⋊Q8 | semidirect |
| 141. C9 | C22×C4⋊Q8 | semidirect |
| 158. C22 | #63506 | direct (N × H) |
| 167. C2 | C2×#63506 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Q8×C9 | 2 |
| C23×Dic18 | 2 |
| C2×#63506 | 2 |
| C22×Dic9⋊C4 | 2 |
| C22×C4×Dic9 | 2 |
| C22×#944 | 3 |