Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
248 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 67 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×Q8×H(3,𝔽3) | C2 | semidirect |
| 3. #3755⋊C3 | C2 | semidirect |
| 4. #3756⋊C3 | C2 | semidirect |
| 5. #3748⋊C3 | C2 | semidirect |
| 6. #64151 | C3 | semidirect |
| 18. C2×C32×Q8 | D3 | semidirect |
| 19. C2×C32×Q8 | C2×C3 | semidirect |
| 22. #3756 | C2×C3 | semidirect |
| 23. #3755 | C2×C3 | semidirect |
| 24. #3748 | C2×C3 | semidirect |
| 95. H(3,𝔽3) | #137 | semidirect |
| 136. C2×Q8 | (C3⋊D3)⋊C3 | semidirect |
| 163. C32 | #942 | semidirect |
| 164. C32 | C3×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×H(3,𝔽3) | 2 |
| #3828⋊C3 | 2 |
| #3755⋊C3 | 2 |
| #3756⋊C3 | 2 |
| #3748⋊C3 | 2 |
| #64151 | 3 |
| C3×#942 | 3 |