Finite Group DatabasebetaFinite Group DatabasebetaOrder 13856.
24 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Dic1732 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #20294072 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | Q16×C433 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | Dic866 | — | 2 | 1 | no | — |
| 5 | Q8×C433 | — | 2 | 1 | no | — |
| 6 | C8×C433 | C22 | 1 | 1 | yes | characteristic |
| 7 | C4×C433 | — | 4 | 1 | no | — |
| 8 | C4×C433 | D4 | 1 | 1 | yes | characteristic |
| 9 | Dic433 | — | 4 | 1 | no | — |
| 10 | C2×C433 | D8 | 1 | 1 | yes | characteristic |
| 11 | C433 | Q32 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | Q32 | — | 433 | 1 | no | maximal, Sylow |
| 13 | Q16 | — | 433 | 1 | no | — |
| 14 | Q16 | D433 | 1 | 1 | yes | characteristic |
| 15 | C16 | — | 433 | 1 | no | — |
| 16 | Q8 | — | 2 | 1 | no | — |
| 17 | Q8 | — | 866 | 1 | no | — |
| 18 | C8 | C2×D433 | 1 | 1 | yes | characteristic |
| 19 | C4 | — | 4 | 1 | no | — |
| 20 | C4 | — | 1732 | 1 | no | — |
| 21 | C4 | C22⋊D433 | 1 | 1 | yes | characteristic |
| 22 | C2 | #20294082 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. C433 | Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic1732 | 2 |
| #20294072 | 2 |
| Q16×C433 | 2 |
| Q32 | 433 |