Finite Group DatabasebetaFinite Group DatabasebetaOrder 22716.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×C3×C631 | C3 | 1 | 1 | yes | maximal, characteristic |
| 2 | #19150943 | — | 4 | 1 | no | maximal, Hall |
| 3 | C2×C3×C631 | — | 3 | 1 | no | — |
| 4 | C22×C631 | C9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C3×C631 | A4 | 1 | 1 | yes | characteristic |
| 6 | C2×C631 | — | 3 | 1 | no | — |
| 7 | C631 | C22⋊C9 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 8 | C22⋊C9 | — | 631 | 1 | no | maximal, Hall |
| 9 | C22×C3 | C631⋊C3 | 1 | 1 | yes | characteristic |
| 10 | C9 | — | 2524 | 1 | no | Sylow |
| 11 | C2×C3 | — | 3 | 1 | no | — |
| 12 | C22 | #19150943 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 13 | C3 | C22⋊(C631⋊C3) | 1 | 1 | yes | characteristic |
| 14 | C2 | — | 3 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊(C631⋊C3) |
| commutator, hypocenter | C22×C631 | C9 |
| Fitting, socle, prime radical, cosocle | C22×C3×C631 | C3 |
| LCS | G ▷ C22×C631 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C22×C631 | C9 | semidirect |
| 7. C631 | C22⋊C9 | semidirect |
| 12. C22 | #19150943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C631 | 3 |
| #19150943 | 4 |
| C22⋊C9 | 631 |