Finite Group DatabasebetaFinite Group DatabasebetaOrder 9516.
24 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C13×D61⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #15691761 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C13×C61⋊C3 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C13×D61 | C2×C3 | 1 | 1 | yes | characteristic |
| 5 | C13×C61 | C3×C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | #6923⋊C3 | — | 13 | 1 | no | maximal, Hall |
| 7 | D61⋊C3 | D13 | 1 | 1 | yes | characteristic |
| 8 | #6923 | — | 13 | 1 | no | Hall |
| 9 | C61⋊C3 | Dic13 | 1 | 1 | yes | characteristic, complemented, Hall |
| 10 | C3×Dic13 | — | 61 | 1 | no | maximal, Hall |
| 11 | D61 | C3×D13 | 1 | 1 | yes | characteristic |
| 12 | C2×C3×C13 | — | 61 | 1 | no | — |
| 13 | C61 | C3×Dic13 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | Dic13 | — | 61 | 1 | no | Hall |
| 15 | C3×C13 | — | 61 | 1 | no | Hall |
| 16 | C2×C13 | — | 61 | 1 | no | — |
| 17 | C13 | #6923⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 18 | C3×C4 | — | 793 | 1 | no | Hall |
| 19 | C2×C3 | — | 61 | 1 | no | — |
| 20 | C4 | — | 793 | 1 | no | Sylow |
| 21 | C3 | — | 61 | 1 | no | Sylow |
| 22 | C2 | — | 61 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C61 | C3×C4 |
| prime radical | C13×D61⋊C3 | C2 |
| cosocle | C13×D61 | C2×C3 |
| LCS | G ▷ C13×C61 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15691761 | C3 | semidirect |
| 3. C13×C61⋊C3 | C4 | semidirect |
| 5. C13×C61 | C3×C4 | semidirect |
| 9. C61⋊C3 | Dic13 | semidirect |
| 13. C61 | C3×Dic13 | semidirect |
| 17. C13 | #6923⋊C3 | semidirect |