Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
376 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 3. C4⋊((C3⋊Dic3)⋊C3) | C2 | semidirect |
| 4. #88449 | C2 | semidirect |
| 9. C4×#272 | C4 | semidirect |
| 15. C4⋊(C3⋊Dic3) | D3 | semidirect |
| 22. C4×H(3,𝔽3) | C2×C4 | semidirect |
| 23. #1084 | C2×C4 | semidirect |
| 41. #272 | C4⋊C4 | semidirect |
| 61. C32×C4 | C4×D3 | semidirect |
| 67. H(3,𝔽3) | C2×C4⋊C4 | semidirect |
| 119. C32 | D3×C4⋊C4 | semidirect |
| 144. 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 |
| #88449 | 2 |
| D3×C4⋊Dic3 | 3 |