Finite Group DatabasebetaFinite Group DatabasebetaOrder 10784.
156 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×Dic674 | C2 | 1 | 12 | yes | maximal, direct product factor |
| 2 | C22×Dic337 | C2 | 1 | 2 | yes | maximal |
| 3 | C22×C4×C337 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | Dic674 | C22 | 1 | 16 | yes | direct product factor |
| 5 | C2×Dic337 | C22 | 1 | 12 | yes | — |
| 6 | C23×C337 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×C4×C337 | C22 | 1 | 6 | yes | — |
| 8 | C22×C337 | Q8 | 1 | 4 | yes | complemented |
| 9 | C22×C337 | C23 | 1 | 3 | yes | — |
| 10 | C4×C337 | C23 | 1 | 4 | yes | — |
| 11 | Dic337 | C23 | 1 | 8 | yes | — |
| 12 | C2×C337 | C2×Q8 | 1 | 6 | yes | complemented |
| 13 | C2×C337 | C24 | 1 | 1 | yes | characteristic |
| 14 | C337 | C22×Q8 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | C22×Q8 | — | 337 | 1 | no | maximal, Sylow |
| 16 | C2×Q8 | — | 337 | 12 | no | — |
| 17 | C22×C4 | — | 337 | 2 | no | — |
| 18 | C22×C4 | D337 | 1 | 1 | yes | characteristic |
| 19 | C23 | C2×D337 | 1 | 1 | yes | characteristic |
| 20 | Q8 | — | 337 | 16 | no | — |
| 21 | C2×C4 | — | 337 | 12 | no | — |
| 22 | C2×C4 | C2×D337 | 1 | 6 | yes | — |
| 23 | C22 | Dic674 | 1 | 4 | yes | direct product factor |
| 24 | C22 | C22×D337 | 1 | 3 | yes | — |
| 25 | C4 | — | 337 | 8 | no | — |
| 26 | C4 | C22×D337 | 1 | 4 | yes | — |
| 27 | C2 | C2×Dic674 | 1 | 6 | yes | direct product factor |
| 28 | C2 | C23×D337 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Dic674 | C2 | direct (N × H) |
| 4. Dic674 | C22 | direct (N × H) |
| 8. C22×C337 | Q8 | semidirect |
| 12. C2×C337 | C2×Q8 | semidirect |
| 14. C337 | C22×Q8 | semidirect |
| 23. C22 | Dic674 | direct (N × H) |
| 27. C2 | C2×Dic674 | direct (N × H) |