Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
316 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 1. C2×C3×D36 | C2 | semidirect |
| 2. C2×#6192 | C2 | semidirect |
| 3. C2×#6192 | C2 | semidirect |
| 4. C2×Dic3×D9 | C2 | semidirect |
| 5. #88536 | C2 | semidirect |
| 6. C9×Dic3⋊C4 | C2 | semidirect |
| 7. (C2×D9)⋊Dic3 | C2 | semidirect |
| 30. C2×D36 | D3 | semidirect |
| 45. C2×C3×D9 | D4 | semidirect |
| 49. C9×Dic3 | D4 | semidirect |
| 97. Dic3⋊C4 | D9 | semidirect |
| 125. C2×D9 | #67 | semidirect |
| 133. C3×C9 | #121 | semidirect |
| 215. Dic3 | D36 | semidirect |
| 218. C9 | #939 | semidirect |
| 261. C3 | #63457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D36 | 2 |
| C2×#6192 | 2 |
| C2×Dic3×D9 | 2 |
| #88536 | 2 |
| C9×Dic3⋊C4 | 2 |
| (C2×D9)⋊Dic3 | 2 |
| #63886 | 3 |
| #63457 | 3 |