Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
238 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 13. C3×Dic12 | C4 | semidirect |
| 54. Dic12 | Dic3 | direct (N × H) |
| 61. C3×Dic3 | Q16 | semidirect |
| 116. Dic3 | Dic12 | direct (N × H) |
| 117. C32 | C4×Q16 | semidirect |
| 144. C3 | C4×Dic12 | semidirect |
| 145. C3 | Dic3×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic12 | 2 |
| Dic3×Dic6 | 2 |
| #63645 | 2 |
| C3×C8×Dic3 | 2 |
| #63566 | 2 |
| Dic3×Q16 | 3 |
| C4×Dic12 | 3 |