Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
30 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Dic1592 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C199⋊C32 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | Q32×C199 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | Dic796 | — | 2 | 1 | no | — |
| 5 | Q16×C199 | — | 2 | 1 | no | — |
| 6 | C16×C199 | C22 | 1 | 1 | yes | characteristic |
| 7 | Dic398 | — | 4 | 1 | no | — |
| 8 | Q8×C199 | — | 4 | 1 | no | — |
| 9 | C8×C199 | D4 | 1 | 1 | yes | characteristic |
| 10 | C4×C199 | — | 8 | 1 | no | — |
| 11 | C4×C199 | D8 | 1 | 1 | yes | characteristic |
| 12 | Dic199 | — | 8 | 1 | no | — |
| 13 | C2×C199 | D16 | 1 | 1 | yes | characteristic |
| 14 | C199 | Q64 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | Q64 | — | 199 | 1 | no | maximal, Sylow |
| 16 | Q32 | — | 199 | 1 | no | — |
| 17 | Q32 | D199 | 1 | 1 | yes | characteristic |
| 18 | C32 | — | 199 | 1 | no | — |
| 19 | Q16 | — | 2 | 1 | no | — |
| 20 | Q16 | — | 398 | 1 | no | — |
| 21 | C16 | C2×D199 | 1 | 1 | yes | characteristic |
| 22 | Q8 | — | 4 | 1 | no | — |
| 23 | Q8 | — | 796 | 1 | no | — |
| 24 | C8 | C22⋊D199 | 1 | 1 | yes | characteristic |
| 25 | C4 | — | 8 | 1 | no | — |
| 26 | C4 | — | 1592 | 1 | no | — |
| 27 | C4 | #15691871 | 1 | 1 | yes | characteristic |
| 28 | C2 | #20263896 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. C199 | Q64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic1592 | 2 |
| C199⋊C32 | 2 |
| Q32×C199 | 2 |
| Q64 | 199 |