Finite Group DatabasebetaFinite Group DatabasebetaOrder 8991.
42 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #15688521 | C3 | 1 | 2 | yes | maximal |
| 2 | C9×#66524 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C37×#733 | C3 | 1 | 1 | yes | maximal, characteristic |
| 4 | 3−1+2×C37 | — | 3 | 1 | no | — |
| 5 | C3×C9×C37 | C32 | 1 | 1 | yes | characteristic |
| 6 | #11758608 | — | 3 | 2 | no | — |
| 7 | C3×#66524 | — | 3 | 1 | no | — |
| 8 | C32×C37 | H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 9 | C9×C37 | — | 3 | 1 | no | — |
| 10 | C9×C37 | — | 9 | 1 | no | — |
| 11 | #66524 | — | 3 | 3 | no | — |
| 12 | #66524 | — | 9 | 2 | no | — |
| 13 | #6880 | — | 37 | 1 | no | maximal, Sylow |
| 14 | C3×C37 | — | 3 | 1 | no | — |
| 15 | C3×C37 | #732 | 1 | 1 | yes | characteristic |
| 16 | #733 | — | 37 | 2 | no | — |
| 17 | #733 | C37⋊C3 | 1 | 1 | yes | characteristic |
| 18 | C92 | — | 37 | 1 | no | — |
| 19 | C37 | #6880 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 20 | 3−1+2 | — | 3 | 1 | no | — |
| 21 | 3−1+2 | — | 111 | 2 | no | — |
| 22 | C3×C9 | — | 111 | 1 | no | — |
| 23 | C3×C9 | C3×C37⋊C3 | 1 | 1 | yes | characteristic |
| 24 | C32 | C32⋊(C37⋊C3) | 1 | 1 | yes | characteristic |
| 25 | C9 | — | 3 | 1 | no | — |
| 26 | C9 | — | 9 | 1 | no | — |
| 27 | C9 | — | 333 | 2 | no | — |
| 28 | C9 | — | 111 | 3 | no | — |
| 29 | C3 | — | 3 | 1 | no | — |
| 30 | C3 | #15688518 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 19. C37 | #6880 | semidirect |