Finite Group DatabasebetaFinite Group DatabasebetaOrder 30861.
110 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #23779840 | C3 | 1 | 8 | yes | maximal, complemented |
| 2 | C3×#16812178 | C3 | 1 | 4 | yes | maximal, complemented |
| 3 | #737×C127 | C3 | 1 | 1 | yes | maximal, characteristic |
| 4 | #16812178 | C32 | 1 | 8 | yes | — |
| 5 | #16812178 | C32 | 1 | 1 | yes | characteristic |
| 6 | 3−1+2×C127 | C9 | 1 | 8 | yes | — |
| 7 | H(3,𝔽3)×C127 | C9 | 1 | 1 | yes | characteristic |
| 8 | C3×C9×C127 | C32 | 1 | 4 | yes | — |
| 9 | C32×C127 | C3×C9 | 1 | 4 | yes | — |
| 10 | C9×C127 | C3×C9 | 1 | 8 | yes | — |
| 11 | C9×C127 | C33 | 1 | 1 | yes | characteristic |
| 12 | C3×C127 | — | 3 | 4 | no | — |
| 13 | C3×C127 | C32×C9 | 1 | 1 | yes | characteristic |
| 14 | #6903 | — | 127 | 1 | no | maximal, Sylow |
| 15 | C127 | #6903 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | #737 | C127⋊C3 | 1 | 1 | yes | characteristic |
| 17 | C27⋊C3 | — | 127 | 8 | no | — |
| 18 | C3×C27 | — | 127 | 4 | no | — |
| 19 | 3−1+2 | #11765917 | 1 | 8 | yes | — |
| 20 | H(3,𝔽3) | #11765917 | 1 | 1 | yes | characteristic |
| 21 | C3×C9 | C3×C127⋊C3 | 1 | 4 | yes | — |
| 22 | C27 | — | 127 | 1 | no | — |
| 23 | C27 | — | 127 | 8 | no | — |
| 24 | C32 | C3×#11765917 | 1 | 4 | yes | — |
| 25 | C9 | C3×#11765917 | 1 | 8 | yes | — |
| 26 | C9 | C32×C127⋊C3 | 1 | 1 | yes | characteristic |
| 27 | C3 | — | 3 | 4 | no | — |
| 28 | C3 | C32×#11765917 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23779840 | C3 | semidirect |
| 2. C3×#16812178 | C3 | semidirect |
| 15. C127 | #6903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23779840 | 3 |
| C3×#16812178 | 3 |
| #737×C127 | 3 |
| #6903 | 127 |