Finite Group DatabasebetaFinite Group DatabasebetaOrder 30861.
166 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 50 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×#16812184 | C3 | semidirect |
| 2. C3×#16812183 | C3 | semidirect |
| 3. C3×#16812182 | C3 | semidirect |
| 5. C3×C9×C127⋊C3 | C3 | semidirect |
| 6. C32⋊#11765917 | C3 | semidirect |
| 7. #23779831 | C3 | semidirect |
| 8. #23779831 | C3 | semidirect |
| 9. #23779831 | C3 | semidirect |
| 10. #23779831 | C3 | semidirect |
| 11. #23779831 | C3 | semidirect |
| 12. #23779831 | C3 | semidirect |
| 13. C32⋊C9×C127 | C3 | semidirect |
| 48. C3×C127⋊C3 | 3−1+2 | semidirect |
| 57. #11765917 | H(3,𝔽3) | semidirect |
| 67. C127 | C9⋊H(3,𝔽3) | semidirect |
| 80. C32⋊C9 | C127⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812184 | 3 |
| C3×#16812183 | 3 |
| C3×#16812182 | 3 |
| C3×C32⋊(C127⋊C3) | 3 |
| C3×C9×C127⋊C3 | 3 |
| C32⋊#11765917 | 3 |
| #23779831 | 3 |
| C32⋊C9×C127 | 3 |
| C9⋊H(3,𝔽3) | 127 |