Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
276 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 77 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 | direct (N × H) |
| 4. C2×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 5. C2×#3755 | C3 | semidirect |
| 9. Q8×H(3,𝔽3) | C22 | semidirect |
| 14. (C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 16. C2×C32×Q8 | D3 | semidirect |
| 17. C2×C32×Q8 | C2×C3 | semidirect |
| 20. #3755 | C2×C3 | semidirect |
| 21. C2×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 39. C32×Q8 | C2×D3 | semidirect |
| 40. C32×Q8 | C22×C3 | semidirect |
| 51. C3⋊(C3⋊C8) | C22×C3 | semidirect |
| 53. C2×H(3,𝔽3) | SD16 | semidirect |
| 86. H(3,𝔽3) | C2×SD16 | semidirect |
| 117. C2×C32 | #215 | semidirect |
| 118. C2×C32 | C3×SD16 | semidirect |
| 123. C2×Q8 | (C3⋊D3)⋊C3 | semidirect |
| 150. C32 | C2×#215 | semidirect |
| 151. C32 | C2×C3×SD16 | semidirect |
| 154. Q8 | C2×(C3⋊D3)⋊C3 | semidirect |
| 182. C2 | #3755⋊C3 | direct (N × H) |
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 |
| C2×C4⋊((C3⋊D3)⋊C3) | 2 |
| #3755⋊C3 | 2 |
| C2×(C3⋊(C3⋊C8))⋊C3 | 2 |
| C2×#3755 | 3 |
| C2×C3×#215 | 3 |