Finite Group DatabasebetaFinite Group DatabasebetaOrder 7092.
36 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C32×C197 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×C4×C197 | C3 | 1 | 4 | yes | maximal, direct product factor |
| 3 | C32×C197 | C4 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 4 | C2×C3×C197 | C2×C3 | 1 | 4 | yes | — |
| 5 | C4×C197 | C32 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 6 | C3×C197 | C3×C4 | 1 | 4 | yes | direct product factor |
| 7 | C2×C197 | C2×C32 | 1 | 1 | yes | characteristic |
| 8 | C197 | C32×C4 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 9 | C32×C4 | C197 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 10 | C2×C32 | C2×C197 | 1 | 1 | yes | characteristic |
| 11 | C3×C4 | C3×C197 | 1 | 4 | yes | direct product factor |
| 12 | C32 | C4×C197 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 13 | C2×C3 | C2×C3×C197 | 1 | 4 | yes | — |
| 14 | C4 | C32×C197 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 15 | C3 | C3×C4×C197 | 1 | 4 | yes | direct product factor |
| 16 | C2 | C2×C32×C197 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C2 | C2×C32×C197 |
| socle | C2×C32×C197 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C4×C197 | C3 | direct (N × H) |
| 3. C32×C197 | C4 | direct (N × H) |
| 5. C4×C197 | C32 | direct (N × H) |
| 6. C3×C197 | C3×C4 | direct (N × H) |
| 8. C197 | C32×C4 | direct (N × H) |
| 9. C32×C4 | C197 | direct (N × H) |
| 11. C3×C4 | C3×C197 | direct (N × H) |
| 12. C32 | C4×C197 | direct (N × H) |
| 14. C4 | C32×C197 | direct (N × H) |
| 15. C3 | C3×C4×C197 | direct (N × H) |