Finite Group DatabasebetaFinite Group DatabasebetaOrder 35008.
30 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Dic4376 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C547⋊C32 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | Q32×C547 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | Dic2188 | — | 2 | 1 | no | — |
| 5 | Q16×C547 | — | 2 | 1 | no | — |
| 6 | C16×C547 | C22 | 1 | 1 | yes | characteristic |
| 7 | Dic1094 | — | 4 | 1 | no | — |
| 8 | Q8×C547 | — | 4 | 1 | no | — |
| 9 | C8×C547 | D4 | 1 | 1 | yes | characteristic |
| 10 | C4×C547 | — | 8 | 1 | no | — |
| 11 | C4×C547 | D8 | 1 | 1 | yes | characteristic |
| 12 | Dic547 | — | 8 | 1 | no | — |
| 13 | C2×C547 | D16 | 1 | 1 | yes | characteristic |
| 14 | C547 | Q64 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | Q64 | — | 547 | 1 | no | maximal, Sylow |
| 16 | Q32 | — | 547 | 1 | no | — |
| 17 | Q32 | D547 | 1 | 1 | yes | characteristic |
| 18 | C32 | — | 547 | 1 | no | — |
| 19 | Q16 | — | 2 | 1 | no | — |
| 20 | Q16 | — | 1094 | 1 | no | — |
| 21 | C16 | C2×D547 | 1 | 1 | yes | characteristic |
| 22 | Q8 | — | 4 | 1 | no | — |
| 23 | Q8 | — | 2188 | 1 | no | — |
| 24 | C8 | C22⋊D547 | 1 | 1 | yes | characteristic |
| 25 | C4 | — | 8 | 1 | no | — |
| 26 | C4 | — | 4376 | 1 | no | — |
| 27 | C4 | #22576761 | 1 | 1 | yes | characteristic |
| 28 | C2 | #31775943 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. C547 | Q64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic4376 | 2 |
| C547⋊C32 | 2 |
| Q32×C547 | 2 |
| Q64 | 547 |