Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
383 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 383 conjugacy classes of subgroups — too many to draw. Only its 64 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×C4⋊#272 | C2 | semidirect |
| 2. C2×C4×(C3⋊D3)⋊C3 | C2 | semidirect |
| 3. C2×#6200 | C2 | semidirect |
| 4. C4⋊((C3⋊Dic3)⋊C3) | C2 | semidirect |
| 5. #88451 | C2 | semidirect |
| 16. C2×C4×C3⋊D3 | D3 | semidirect |
| 23. C4⋊(C3⋊Dic3) | D3 | semidirect |
| 33. C2×(C3⋊D3)⋊C3 | D4 | semidirect |
| 34. C4×H(3,𝔽3) | D4 | semidirect |
| 85. C2×C3⋊D3 | D12 | semidirect |
| 99. C32×C4 | D12 | semidirect |
| 100. C32×C4 | #67 | semidirect |
| 106. H(3,𝔽3) | #121 | semidirect |
| 189. C32 | #895 | semidirect |
| 190. C32 | #930 | semidirect |
| 227. C4 | #6200 | 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×C4×(C3⋊D3)⋊C3 | 2 |
| C2×#6200 | 2 |
| C4⋊((C3⋊Dic3)⋊C3) | 2 |
| #88451 | 2 |
| #63916 | 3 |
| #63908 | 3 |