Finite Group DatabasebetaFinite Group DatabasebetaOrder 36693.
50 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C32⋊(C151⋊C9) | C3 | 1 | 3 | yes | maximal |
| 2 | C32⋊C9×C151 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3×C151⋊C9 | — | 3 | 3 | no | — |
| 4 | C33×C151 | C32 | 1 | 1 | yes | characteristic |
| 5 | C3×C9×C151 | — | 3 | 1 | no | — |
| 6 | C32×C151 | — | 3 | 1 | no | — |
| 7 | C32×C151 | — | 3 | 1 | no | — |
| 8 | C32×C151 | — | 3 | 2 | no | — |
| 9 | C32×C151 | H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 10 | C9×C151 | — | 9 | 1 | no | — |
| 11 | C151⋊C9 | — | 9 | 3 | no | — |
| 12 | C3×C151 | — | 9 | 1 | no | — |
| 13 | C3×C151 | #731 | 1 | 1 | yes | characteristic |
| 14 | C3×C151 | #732 | 1 | 1 | yes | characteristic |
| 15 | C3×C151 | #733 | 1 | 2 | yes | — |
| 16 | #6861 | — | 151 | 1 | no | maximal, Sylow |
| 17 | C151 | #6861 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 18 | C32⋊C9 | — | 151 | 3 | no | — |
| 19 | C32⋊C9 | C151⋊C3 | 1 | 1 | yes | characteristic |
| 20 | C33 | C3×C151⋊C3 | 1 | 1 | yes | characteristic |
| 21 | C3×C9 | — | 3 | 1 | no | — |
| 22 | C3×C9 | — | 453 | 3 | no | — |
| 23 | C32 | — | 3 | 1 | no | — |
| 24 | C32 | — | 3 | 1 | no | — |
| 25 | C32 | — | 3 | 2 | no | — |
| 26 | C32 | C32⋊(C151⋊C3) | 1 | 1 | yes | characteristic |
| 27 | C9 | — | 9 | 1 | no | — |
| 28 | C9 | — | 1359 | 3 | no | — |
| 29 | C3 | — | 9 | 1 | no | — |
| 30 | C3 | #27133556 | 1 | 1 | yes | characteristic |
| 31 | C3 | #27133560 | 1 | 1 | yes | characteristic |
| 32 | C3 | #27133561 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 17. C151 | #6861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32⋊(C151⋊C9) | 3 |
| C32⋊C9×C151 | 3 |
| #6861 | 151 |