Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
376 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 376 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 |
|---|---|---|
| 4. #3750⋊C3 | C2 | semidirect |
| 5. #88448 | C2 | semidirect |
| 14. #6199 | C4 | semidirect |
| 19. #3750 | D3 | semidirect |
| 30. (C3⋊Dic3)⋊C3 | C2×C4 | semidirect |
| 51. #272 | C4⋊C4 | semidirect |
| 77. C3⋊Dic3 | C4×D3 | semidirect |
| 83. H(3,𝔽3) | C2×C4⋊C4 | semidirect |
| 146. C32 | D3×C4⋊C4 | 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 |
| #3750⋊C3 | 2 |
| #88448 | 2 |
| D3×Dic3⋊C4 | 3 |