Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
350 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 70 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. #88862 | C3 | semidirect |
| 11. C33×Q8 | D3 | semidirect |
| 12. C33×Q8 | C2×C3 | semidirect |
| 15. C3⋊(C3⋊(C3⋊C8)) | C2×C3 | semidirect |
| 18. Q8×H(3,𝔽3) | D3 | semidirect |
| 41. C3×H(3,𝔽3) | SD16 | semidirect |
| 48. C32×Q8 | C3×D3 | semidirect |
| 49. C32×Q8 | C3⋊D3 | semidirect |
| 94. C33 | #215 | semidirect |
| 95. C33 | C3×SD16 | semidirect |
| 97. H(3,𝔽3) | #215 | semidirect |
| 102. C3×Q8 | (C3⋊D3)⋊C3 | semidirect |
| 148. C32 | C3×#215 | semidirect |
| 149. C32 | #3755 | semidirect |
| 150. Q8 | C3⋊((C3⋊D3)⋊C3) | semidirect |
| 170. C3 | #3755⋊C3 | semidirect |
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 |
| C4⋊(C3⋊((C3⋊D3)⋊C3)) | 2 |
| C3⋊((C3⋊(C3⋊C8))⋊C3) | 2 |
| #88862 | 3 |
| C3×#3755 | 3 |
| #3755⋊C3 | 3 |