Finite Group DatabasebetaFinite Group DatabasebetaOrder 10647.
96 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×C7×C132 | C3 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13095200 | — | 7 | 1 | no | maximal, Hall |
| 3 | C7×C132 | C9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | #11717941 | — | 13 | 14 | no | maximal |
| 5 | C3×C132 | ΓL(1,𝔽8) | 1 | 1 | yes | characteristic |
| 6 | C3×C7×C13 | C13⋊C3 | 1 | 14 | yes | — |
| 7 | C132 | C7⋊C9 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 8 | C13⋊C9 | — | 91 | 14 | no | — |
| 9 | C7×C13 | C13⋊C9 | 1 | 14 | yes | complemented |
| 10 | C7⋊C9 | — | 169 | 1 | no | Hall |
| 11 | C3×C13 | #63270 | 1 | 14 | yes | — |
| 12 | C3×C7 | #92788 | 1 | 1 | yes | characteristic |
| 13 | C13 | #11717941 | 1 | 14 | yes | complemented |
| 14 | C9 | — | 1183 | 1 | no | Sylow |
| 15 | C7 | #13095200 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | C3 | #16813074 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #16813074 |
| commutator, hypocenter | C7×C132 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C7×C132 | C3 |
| LCS | G ▷ C7×C132 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C7×C132 | C9 | semidirect |
| 7. C132 | C7⋊C9 | semidirect |
| 9. C7×C13 | C13⋊C9 | semidirect |
| 13. C13 | #11717941 | semidirect |
| 15. C7 | #13095200 | semidirect |