Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
308 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 74 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. C3×Q8×H(3,𝔽3) | C2 | semidirect |
| 3. C3×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 4. C3×#3755 | C3 | semidirect |
| 6. #3755⋊C3 | C3 | direct (N × H) |
| 11. C33×Q8 | D3 | semidirect |
| 12. C33×Q8 | C2×C3 | semidirect |
| 15. C3×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 18. Q8×H(3,𝔽3) | C2×C3 | semidirect |
| 20. (C3⋊(C3⋊C8))⋊C3 | C2×C3 | semidirect |
| 24. #3755 | C32 | semidirect |
| 41. C3×H(3,𝔽3) | SD16 | semidirect |
| 51. C32×Q8 | C3×D3 | semidirect |
| 52. C32×Q8 | C2×C32 | semidirect |
| 59. C3⋊(C3⋊C8) | C2×C32 | semidirect |
| 103. C33 | #215 | semidirect |
| 104. C33 | C3×SD16 | semidirect |
| 106. H(3,𝔽3) | C3×SD16 | semidirect |
| 112. C3×Q8 | (C3⋊D3)⋊C3 | semidirect |
| 166. C32 | C3×#215 | semidirect |
| 167. C32 | C32×SD16 | semidirect |
| 168. Q8 | C3×(C3⋊D3)⋊C3 | semidirect |
| 190. C3 | #3755⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×H(3,𝔽3) | 2 |
| C3×C4⋊((C3⋊D3)⋊C3) | 2 |
| C3×(C3⋊(C3⋊C8))⋊C3 | 2 |
| C3×#3755 | 3 |
| C32×#215 | 3 |
| #3755⋊C3 | 3 |