Finite Group DatabasebetaFinite Group DatabasebetaOrder 11296.
38 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #19150746 | C2 | 1 | 2 | yes | maximal |
| 2 | C2×Dic706 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #15667732 | — | 2 | 2 | no | — |
| 4 | Dic706 | — | 2 | 2 | no | — |
| 5 | C2×Dic353 | C4 | 1 | 1 | yes | characteristic |
| 6 | C2×Dic353 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×C4×C353 | C4 | 1 | 1 | yes | characteristic |
| 8 | C22×C353 | C2×C4 | 1 | 1 | yes | characteristic |
| 9 | C4×C353 | — | 2 | 1 | no | — |
| 10 | Dic353 | — | 2 | 1 | no | — |
| 11 | Dic353 | D4 | 1 | 2 | yes | — |
| 12 | C2×C353 | — | 2 | 1 | no | — |
| 13 | C2×C353 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 14 | C353 | #101 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | #101 | — | 353 | 1 | no | maximal, Sylow |
| 16 | C2×Q8 | — | 353 | 1 | no | — |
| 17 | M16 | — | 353 | 2 | no | — |
| 18 | Q8 | — | 706 | 2 | no | — |
| 19 | C2×C4 | — | 353 | 1 | no | — |
| 20 | C2×C4 | — | 353 | 1 | no | — |
| 21 | C2×C4 | #13083443 | 1 | 1 | yes | characteristic |
| 22 | C8 | — | 706 | 2 | no | — |
| 23 | C22 | C2×#13083443 | 1 | 1 | yes | characteristic |
| 24 | C4 | — | 2 | 1 | no | — |
| 25 | C4 | — | 353 | 2 | no | — |
| 26 | C4 | — | 706 | 1 | no | — |
| 27 | C2 | — | 2 | 1 | no | — |
| 28 | C2 | C22⋊#13083443 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. C353 | #101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19150746 | 2 |
| C2×Dic706 | 2 |
| #101 | 353 |