Finite Group DatabasebetaFinite Group Databasebeta← C3×C3⋊((C3⋊(C3⋊C8))⋊C3) #14517868
Order 1944.
855 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 855 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 2. C3×C3⋊(C3⋊(C3⋊C8)) | C3 | semidirect |
| 4. C3⋊((C3⋊(C3⋊C8))⋊C3) | C3 | direct (N × H) |
| 15. C32×H(3,𝔽3) | C8 | semidirect |
| 16. C3⋊(C3⋊(C3⋊C8)) | C32 | semidirect |
| 55. C34 | C3⋊C8 | semidirect |
| 56. C34 | C3×C8 | semidirect |
| 60. C3×H(3,𝔽3) | C3⋊C8 | semidirect |
| 61. C3×H(3,𝔽3) | C3×C8 | semidirect |
| 132. C33 | C3×C3⋊C8 | semidirect |
| 133. C33 | C3×C3⋊C8 | semidirect |
| 134. C33 | C3⋊(C3⋊C8) | semidirect |
| 135. C33 | C32×C8 | semidirect |
| 139. H(3,𝔽3) | C3×C3⋊C8 | semidirect |
| 200. C32 | (C3⋊(C3⋊C8))⋊C3 | semidirect |
| 202. C32 | C32×C3⋊C8 | semidirect |
| 204. C32 | C3×C3⋊(C3⋊C8) | semidirect |
| 224. C3 | C3×(C3⋊(C3⋊C8))⋊C3 | semidirect |
| 225. C3 | C3⋊((C3⋊(C3⋊C8))⋊C3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×H(3,𝔽3) | 2 |
| C3×C3⋊(C3⋊(C3⋊C8)) | 3 |
| C32×C3⋊(C3⋊C8) | 3 |
| C3⋊((C3⋊(C3⋊C8))⋊C3) | 3 |
| C3×(C3⋊(C3⋊C8))⋊C3 | 3 |