Finite Group DatabasebetaFinite Group DatabasebetaOrder 9872.
18 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Dic1234 | C2 | 1 | 2 | yes | maximal |
| 2 | C8×C617 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C4×C617 | C22 | 1 | 1 | yes | characteristic |
| 4 | Dic617 | — | 2 | 2 | no | — |
| 5 | C2×C617 | D4 | 1 | 1 | yes | characteristic |
| 6 | C617 | Q16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 7 | Q16 | — | 617 | 1 | no | maximal, Sylow |
| 8 | Q8 | — | 617 | 2 | no | — |
| 9 | C8 | D617 | 1 | 1 | yes | characteristic |
| 10 | C4 | — | 1234 | 2 | no | — |
| 11 | C4 | C2×D617 | 1 | 1 | yes | characteristic |
| 12 | C2 | D2468 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C617 | Q16 | semidirect |