Finite Group DatabasebetaFinite Group DatabasebetaOrder 10768.
38 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Dic1346 | C2 | 1 | 4 | yes | maximal, direct product factor |
| 2 | C2×Dic673 | C2 | 1 | 2 | yes | maximal |
| 3 | C2×C4×C673 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C22×C673 | C22 | 1 | 1 | yes | characteristic |
| 5 | C4×C673 | C22 | 1 | 2 | yes | — |
| 6 | Dic673 | C22 | 1 | 4 | yes | — |
| 7 | C2×C673 | Q8 | 1 | 2 | yes | complemented |
| 8 | C2×C673 | C23 | 1 | 1 | yes | characteristic |
| 9 | C673 | C2×Q8 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | C2×Q8 | — | 673 | 1 | no | maximal, Sylow |
| 11 | Q8 | — | 673 | 4 | no | — |
| 12 | C2×C4 | — | 673 | 2 | no | — |
| 13 | C2×C4 | D673 | 1 | 1 | yes | characteristic |
| 14 | C22 | C2×D673 | 1 | 1 | yes | characteristic |
| 15 | C4 | — | 673 | 4 | no | — |
| 16 | C4 | C2×D673 | 1 | 2 | yes | — |
| 17 | C2 | Dic1346 | 1 | 2 | yes | direct product factor |
| 18 | C2 | C22×D673 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Dic1346 | C2 | direct (N × H) |
| 7. C2×C673 | Q8 | semidirect |
| 9. C673 | C2×Q8 | semidirect |
| 17. C2 | Dic1346 | direct (N × H) |