Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
408 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 408 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⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 2. C2×#6198 | C2 | semidirect |
| 3. C4×#1084 | C2 | semidirect |
| 10. C2×C4⋊(C3⋊D3) | D3 | semidirect |
| 18. C4×H(3,𝔽3) | D4 | semidirect |
| 19. #1084 | D4 | semidirect |
| 49. C32×C4 | #67 | semidirect |
| 53. H(3,𝔽3) | #127 | semidirect |
| 93. C32 | #940 | semidirect |
| 112. C4 | #6198 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊((C3⋊D3)⋊C3) | 2 |
| C2×#6198 | 2 |
| C4×#1084 | 2 |
| #63911 | 3 |