Finite Group DatabasebetaFinite Group DatabasebetaOrder 30699.
26 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #23779522 | C3 | 1 | 3 | yes | maximal |
| 2 | C3×C9×C379 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C32×C379 | C32 | 1 | 1 | yes | characteristic |
| 4 | C9×C379 | — | 3 | 1 | no | — |
| 5 | #16811787 | — | 3 | 3 | no | — |
| 6 | C3×C379 | — | 3 | 1 | no | — |
| 7 | C3×C379 | H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 8 | C379 | #733 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | #733 | — | 379 | 1 | no | maximal, Sylow |
| 10 | 3−1+2 | — | 379 | 3 | no | — |
| 11 | C3×C9 | C379⋊C3 | 1 | 1 | yes | characteristic |
| 12 | C32 | C3×C379⋊C3 | 1 | 1 | yes | characteristic |
| 13 | C9 | — | 3 | 1 | no | — |
| 14 | C9 | — | 1137 | 3 | no | — |
| 15 | C3 | — | 3 | 1 | no | — |
| 16 | C3 | C32⋊(C379⋊C3) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C379 | #733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23779522 | 3 |
| C3×C9×C379 | 3 |
| #733 | 379 |