Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
1008 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 240 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 |
|---|---|---|
| 2. C22×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 3. C22×C32×Dic3 | C2 | semidirect |
| 4. #88803 | C2 | direct (N × H) |
| 10. C22×C3×C3⋊D3 | C4 | semidirect |
| 13. C2×C3⋊(C3⋊Dic3) | C22 | semidirect |
| 15. C2×C32×Dic3 | C22 | semidirect |
| 22. C22×C3×Dic3 | D3 | semidirect |
| 32. C2×C3×C3⋊D3 | C2×C4 | semidirect |
| 42. C22×C3⋊D3 | Dic3 | semidirect |
| 57. C2×C3×Dic3 | C2×D3 | semidirect |
| 58. C2×C33 | C22⋊C4 | semidirect |
| 69. C22×Dic3 | C3⋊D3 | semidirect |
| 87. C2×C3⋊D3 | C2×Dic3 | semidirect |
| 98. C33 | C2×C22⋊C4 | semidirect |
| 119. C2×Dic3 | C2×C3⋊D3 | semidirect |
| 124. C2×C32 | (C2×D3)⋊C4 | semidirect |
| 125. C2×C32 | #217 | semidirect |
| 164. C32 | C2×(C2×D3)⋊C4 | semidirect |
| 165. C32 | C2×#217 | semidirect |
| 180. C2×C3 | (C2×D3)⋊Dic3 | semidirect |
| 181. C2×C3 | #3752 | semidirect |
| 200. C3 | C2×(C2×D3)⋊Dic3 | semidirect |
| 201. C3 | C2×#3752 | semidirect |
| 203. C2 | #88803 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C3⋊D3 | 2 |
| C22×C3⋊(C3⋊Dic3) | 2 |
| C22×C32×Dic3 | 2 |
| #88803 | 2 |
| C2×#3752 | 3 |
| C2×(C2×D3)⋊Dic3 | 3 |