Finite Group DatabasebetaFinite Group DatabasebetaOrder 29727.
34 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×C367⋊C9 | C3 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×C367⋊C9 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3×C367⋊C9 | C3 | 1 | 1 | yes | maximal, characteristic |
| 4 | C3×C9×C367 | C3 | 1 | 1 | yes | maximal, characteristic |
| 5 | C32×C367 | C32 | 1 | 1 | yes | characteristic |
| 6 | C9×C367 | — | 3 | 1 | no | — |
| 7 | C367⋊C9 | — | 3 | 1 | no | — |
| 8 | C367⋊C9 | — | 3 | 1 | no | — |
| 9 | C367⋊C9 | C9 | 1 | 3 | yes | complemented |
| 10 | C3×C367 | C3×C9 | 1 | 1 | yes | characteristic |
| 11 | C3×C367 | 3−1+2 | 1 | 1 | yes | characteristic |
| 12 | C3×C367 | 3−1+2 | 1 | 1 | yes | characteristic |
| 13 | C3×C367 | 3−1+2 | 1 | 1 | yes | characteristic |
| 14 | C367 | C9⋊C9 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | C9⋊C9 | — | 367 | 1 | no | maximal, Sylow |
| 16 | C3×C9 | — | 367 | 1 | no | — |
| 17 | C3×C9 | — | 367 | 1 | no | — |
| 18 | C3×C9 | — | 367 | 1 | no | — |
| 19 | C3×C9 | C367⋊C3 | 1 | 1 | yes | characteristic |
| 20 | C32 | C3×C367⋊C3 | 1 | 1 | yes | characteristic |
| 21 | C9 | — | 3 | 1 | no | — |
| 22 | C9 | — | 1101 | 1 | no | — |
| 23 | C9 | — | 1101 | 1 | no | — |
| 24 | C9 | — | 367 | 3 | no | — |
| 25 | C3 | C9×C367⋊C3 | 1 | 1 | yes | characteristic |
| 26 | C3 | #23755306 | 1 | 1 | yes | characteristic |
| 27 | C3 | #23755307 | 1 | 1 | yes | characteristic |
| 28 | C3 | #23755308 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C367⋊C9 | C9 | semidirect |
| 14. C367 | C9⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C367⋊C9 | 3 |
| C3×C9×C367 | 3 |
| C9⋊C9 | 367 |