Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1328 conjugacy classes of subgroups; only the 346 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 346 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. C32×#10587025 | C3 | semidirect |
| 2. C33×#4294 | C3 | semidirect |
| 3. #17987423 | C3 | direct (N × H) |
| 4. C3×C32⋊#4294 | C3 | semidirect |
| 5. C3×C32⋊#4294 | C3 | semidirect |
| 8. C3×#10587025 | C32 | semidirect |
| 13. C32×#4294 | C32 | semidirect |
| 14. C32⋊#4294 | C32 | semidirect |
| 15. C32⋊#4294 | C32 | semidirect |
| 26. C33×C19 | 3−1+2 | semidirect |
| 35. C3×#4294 | H(3,𝔽3) | semidirect |
| 54. C32×C19 | C3×3−1+2 | semidirect |
| 59. #4294 | C3×H(3,𝔽3) | semidirect |
| 75. C3×C19 | C9⋊H(3,𝔽3) | semidirect |
| 84. C33 | #10587025 | semidirect |
| 97. C19 | C3×C9⋊H(3,𝔽3) | semidirect |
| 107. C32 | C3×#10587025 | semidirect |
| 115. C3 | #17987423 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#10587025 | 3 |
| C33×#4294 | 3 |
| #17987423 | 3 |
| C3×C32⋊#4294 | 3 |
| C32×C19×H(3,𝔽3) | 3 |
| C3×C9⋊H(3,𝔽3) | 19 |