Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
32 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Dic2152 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22575359 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | D16×C269 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | Dic1076 | — | 2 | 1 | no | — |
| 5 | D8×C269 | — | 2 | 1 | no | — |
| 6 | C16×C269 | C22 | 1 | 1 | yes | characteristic |
| 7 | Dic538 | — | 4 | 1 | no | — |
| 8 | D4×C269 | — | 4 | 1 | no | — |
| 9 | C8×C269 | D4 | 1 | 1 | yes | characteristic |
| 10 | C22×C269 | — | 8 | 1 | no | — |
| 11 | C4×C269 | D8 | 1 | 1 | yes | characteristic |
| 12 | Dic269 | — | 8 | 1 | no | — |
| 13 | C2×C269 | — | 16 | 1 | no | — |
| 14 | C2×C269 | D16 | 1 | 1 | yes | characteristic |
| 15 | C269 | SD64 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | SD64 | — | 269 | 1 | no | maximal, Sylow |
| 17 | Q32 | — | 269 | 1 | no | — |
| 18 | D16 | D269 | 1 | 1 | yes | characteristic |
| 19 | C32 | — | 269 | 1 | no | — |
| 20 | Q16 | — | 538 | 1 | no | — |
| 21 | D8 | — | 2 | 1 | no | — |
| 22 | C16 | C2×D269 | 1 | 1 | yes | characteristic |
| 23 | Q8 | — | 1076 | 1 | no | — |
| 24 | D4 | — | 4 | 1 | no | — |
| 25 | C8 | C22⋊D269 | 1 | 1 | yes | characteristic |
| 26 | C22 | — | 8 | 1 | no | — |
| 27 | C4 | — | 2152 | 1 | no | — |
| 28 | C4 | #16864387 | 1 | 1 | yes | characteristic |
| 29 | C2 | — | 16 | 1 | no | — |
| 30 | C2 | #22575394 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Dic2152 | C2 | semidirect |
| 2. #22575359 | C2 | semidirect |
| 15. C269 | SD64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic2152 | 2 |
| #22575359 | 2 |
| D16×C269 | 2 |
| SD64 | 269 |