Finite Group DatabasebetaFinite Group DatabasebetaOrder 24867.
40 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C32×C307⋊C3 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22552077 | C3 | 1 | 2 | yes | maximal, complemented |
| 3 | H(3,𝔽3)×C307 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C32×C307 | — | 3 | 1 | no | — |
| 5 | C32×C307 | C32 | 1 | 1 | yes | characteristic |
| 6 | C3×C307⋊C3 | — | 3 | 1 | no | — |
| 7 | C3×C307⋊C3 | — | 3 | 3 | no | — |
| 8 | #14583772 | — | 3 | 2 | no | — |
| 9 | C3×C307 | — | 3 | 1 | no | — |
| 10 | C3×C307 | — | 9 | 1 | no | — |
| 11 | C3×C307 | H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 12 | C307⋊C3 | — | 3 | 3 | no | — |
| 13 | C307 | AΣL(1,𝔽27) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | AΣL(1,𝔽27) | — | 307 | 1 | no | maximal, Sylow |
| 15 | C33 | — | 307 | 1 | no | — |
| 16 | 3−1+2 | — | 307 | 2 | no | — |
| 17 | H(3,𝔽3) | C307⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 18 | C32 | — | 3 | 1 | no | — |
| 19 | C32 | — | 921 | 3 | no | — |
| 20 | C32 | — | 921 | 1 | no | — |
| 21 | C32 | C3×C307⋊C3 | 1 | 1 | yes | characteristic |
| 22 | C9 | — | 921 | 2 | no | — |
| 23 | C3 | — | 3 | 1 | no | — |
| 24 | C3 | — | 9 | 1 | no | — |
| 25 | C3 | — | 921 | 3 | no | — |
| 26 | C3 | C32⋊(C307⋊C3) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C307⋊C3 | C3 | semidirect |
| 2. #22552077 | C3 | semidirect |
| 3. H(3,𝔽3)×C307 | C3 | semidirect |
| 13. C307 | AΣL(1,𝔽27) | semidirect |
| 17. H(3,𝔽3) | C307⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C307⋊C3 | 3 |
| #22552077 | 3 |
| H(3,𝔽3)×C307 | 3 |
| AΣL(1,𝔽27) | 307 |