Finite Group DatabasebetaFinite Group DatabasebetaOrder 9506.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C49×C97 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D7×C97 | — | 7 | 1 | no | maximal |
| 3 | C7×C97 | D7 | 1 | 1 | yes | characteristic |
| 4 | C2×C97 | — | 49 | 1 | no | Hall |
| 5 | D49 | C97 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 6 | C97 | D49 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 7 | C49 | C2×C97 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 8 | D7 | — | 7 | 1 | no | — |
| 9 | C7 | D7×C97 | 1 | 1 | yes | characteristic |
| 10 | C2 | — | 49 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C97 | D49 |
| commutator, cosocle, hypocenter | C49 | C2×C97 |
| Frattini | C7 | D7×C97 |
| Fitting | C49×C97 | C2 |
| socle | C7×C97 | D7 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C49×C97 | C2 | semidirect |
| 5. D49 | C97 | direct (N × H) |
| 6. C97 | D49 | direct (N × H) |
| 7. C49 | C2×C97 | semidirect |