Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
60 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22575514 | C2 | 1 | 2 | yes | maximal |
| 2 | #22575451 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #16864411 | — | 2 | 2 | no | — |
| 4 | C2×Dic538 | C22 | 1 | 1 | yes | characteristic |
| 5 | #16864381 | — | 2 | 2 | no | — |
| 6 | C4×Dic269 | C4 | 1 | 1 | yes | characteristic |
| 7 | C2×Q8×C269 | C4 | 1 | 1 | yes | characteristic |
| 8 | #14524137 | — | 4 | 2 | no | — |
| 9 | Dic538 | — | 4 | 1 | no | — |
| 10 | C2×Dic269 | — | 2 | 1 | no | — |
| 11 | C2×Dic269 | D4 | 1 | 2 | yes | — |
| 12 | Q8×C269 | — | 4 | 1 | no | — |
| 13 | C2×C4×C269 | — | 2 | 1 | no | — |
| 14 | C2×C4×C269 | C2×C4 | 1 | 1 | yes | characteristic |
| 15 | C22×C269 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 16 | C4×C269 | — | 2 | 1 | no | — |
| 17 | C4×C269 | — | 4 | 1 | no | — |
| 18 | Dic269 | — | 2 | 2 | no | — |
| 19 | Dic269 | — | 2 | 2 | no | — |
| 20 | C2×C269 | — | 2 | 1 | no | — |
| 21 | C2×C269 | #99 | 1 | 1 | yes | characteristic |
| 22 | C269 | #356 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 23 | #356 | — | 269 | 1 | no | maximal, Sylow |
| 24 | C4⋊Q8 | — | 269 | 1 | no | — |
| 25 | #101 | — | 269 | 2 | no | — |
| 26 | C2×Q8 | — | 269 | 1 | no | — |
| 27 | C2×Q8 | #11761640 | 1 | 1 | yes | characteristic |
| 28 | M16 | — | 538 | 2 | no | — |
| 29 | C4⋊C4 | — | 538 | 2 | no | — |
| 30 | C42 | — | 269 | 1 | no | — |
| 31 | Q8 | — | 4 | 1 | no | — |
| 32 | Q8 | — | 1076 | 1 | no | — |
| 33 | C2×C4 | — | 2 | 1 | no | — |
| 34 | C2×C4 | — | 269 | 2 | no | — |
| 35 | C2×C4 | — | 538 | 1 | no | — |
| 36 | C2×C4 | C2×#11761640 | 1 | 1 | yes | characteristic |
| 37 | C8 | — | 1076 | 2 | no | — |
| 38 | C22 | C22⋊#11761640 | 1 | 1 | yes | characteristic |
| 39 | C4 | — | 2 | 1 | no | — |
| 40 | C4 | — | 4 | 1 | no | — |
| 41 | C4 | — | 538 | 2 | no | — |
| 42 | C4 | — | 538 | 2 | no | — |
| 43 | C2 | — | 2 | 1 | no | — |
| 44 | C2 | #22575511 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 22. C269 | #356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22575514 | 2 |
| #22575451 | 2 |
| #356 | 269 |