Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
54 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22582510 | C3 | 1 | 3 | yes | maximal |
| 2 | C37×#6864 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | #15688521 | — | 3 | 3 | no | — |
| 4 | C3×C27×C37 | — | 3 | 1 | no | — |
| 5 | C92×C37 | C32 | 1 | 1 | yes | characteristic |
| 6 | C3×C9×C37 | — | 3 | 1 | no | — |
| 7 | C3×C9×C37 | H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 8 | #11758608 | — | 9 | 3 | no | — |
| 9 | C27×C37 | — | 3 | 3 | no | — |
| 10 | #10624541 | — | 37 | 1 | no | maximal, Sylow |
| 11 | C32×C37 | #732 | 1 | 1 | yes | characteristic |
| 12 | C9×C37 | — | 3 | 1 | no | — |
| 13 | C9×C37 | — | 9 | 1 | no | — |
| 14 | #66524 | — | 27 | 3 | no | — |
| 15 | #6880 | — | 37 | 3 | no | — |
| 16 | #6864 | C37⋊C3 | 1 | 1 | yes | characteristic |
| 17 | C3×C37 | — | 3 | 1 | no | — |
| 18 | C3×C37 | #6879 | 1 | 1 | yes | characteristic |
| 19 | #733 | — | 111 | 3 | no | — |
| 20 | C3×C27 | — | 3 | 1 | no | — |
| 21 | C92 | C3×C37⋊C3 | 1 | 1 | yes | characteristic |
| 22 | C37 | #10624541 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 23 | 3−1+2 | — | 333 | 3 | no | — |
| 24 | C3×C9 | — | 3 | 1 | no | — |
| 25 | C3×C9 | C32⋊(C37⋊C3) | 1 | 1 | yes | characteristic |
| 26 | C27 | — | 3 | 3 | no | — |
| 27 | C32 | #15688519 | 1 | 1 | yes | characteristic |
| 28 | C9 | — | 3 | 1 | no | — |
| 29 | C9 | — | 9 | 1 | no | — |
| 30 | C9 | — | 999 | 3 | no | — |
| 31 | C3 | — | 3 | 1 | no | — |
| 32 | C3 | #22582507 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 22. C37 | #10624541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582510 | 3 |
| C37×#6864 | 3 |
| #10624541 | 37 |