Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
383 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 383 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×#6199 | C2 | semidirect |
| 3. C4⋊((C3⋊Dic3)⋊C3) | C2 | semidirect |
| 4. C4×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 5. #88451 | C2 | semidirect |
| 10. C4⋊#272 | C4 | semidirect |
| 20. C4⋊(C3⋊Dic3) | D3 | semidirect |
| 21. C4×C3⋊Dic3 | D3 | semidirect |
| 29. C2×#272 | C2×C4 | semidirect |
| 30. C4×H(3,𝔽3) | C2×C4 | semidirect |
| 33. (C3⋊Dic3)⋊C3 | D4 | semidirect |
| 87. C32×C4 | C4×D3 | semidirect |
| 88. C32×C4 | C4×D3 | semidirect |
| 91. C3⋊Dic3 | D12 | semidirect |
| 96. H(3,𝔽3) | C4×D4 | semidirect |
| 168. C32 | C4×D12 | semidirect |
| 169. C32 | #893 | semidirect |
| 200. C4 | #6199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#272 | 2 |
| C2×#6199 | 2 |
| C4⋊((C3⋊Dic3)⋊C3) | 2 |
| C4×(C3⋊Dic3)⋊C3 | 2 |
| #88451 | 2 |
| #63898 | 3 |
| Dic3×D12 | 3 |