Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
46 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #17984162 | C2 | 1 | 2 | yes | maximal |
| 2 | C4×#11764040 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #14555513 | — | 2 | 2 | no | — |
| 4 | C2×#11764040 | C4 | 1 | 1 | yes | characteristic |
| 5 | C2×#11764040 | C22 | 1 | 1 | yes | characteristic |
| 6 | C42×C137 | C4 | 1 | 1 | yes | characteristic |
| 7 | #11764040 | C8 | 1 | 2 | yes | — |
| 8 | #11764040 | D4 | 1 | 1 | yes | characteristic |
| 9 | #11764040 | Q8 | 1 | 1 | yes | characteristic |
| 10 | C2×C4×C137 | — | 2 | 1 | no | — |
| 11 | C2×C4×C137 | C2×C4 | 1 | 1 | yes | characteristic |
| 12 | C22×C137 | M16 | 1 | 1 | yes | characteristic |
| 13 | C4×C137 | — | 2 | 2 | no | — |
| 14 | C4×C137 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 15 | C4×C137 | C2×C8 | 1 | 1 | yes | characteristic |
| 16 | C2×C137 | — | 2 | 1 | no | — |
| 17 | C2×C137 | C4⋊C8 | 1 | 1 | yes | characteristic |
| 18 | C137 | #364 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 19 | #364 | — | 137 | 1 | no | maximal, Sylow |
| 20 | M32 | — | 137 | 2 | no | — |
| 21 | C4×C8 | — | 137 | 1 | no | — |
| 22 | C2×C8 | — | 137 | 1 | no | — |
| 23 | C2×C8 | — | 137 | 1 | no | — |
| 24 | C42 | #10587739 | 1 | 1 | yes | characteristic |
| 25 | C16 | — | 274 | 2 | no | — |
| 26 | C2×C4 | — | 2 | 1 | no | — |
| 27 | C2×C4 | C2×#10587739 | 1 | 1 | yes | characteristic |
| 28 | C8 | — | 137 | 1 | no | — |
| 29 | C8 | — | 137 | 1 | no | — |
| 30 | C8 | — | 137 | 2 | no | — |
| 31 | C22 | #14555519 | 1 | 1 | yes | characteristic |
| 32 | C4 | — | 2 | 2 | no | — |
| 33 | C4 | C4⋊#10587739 | 1 | 1 | yes | characteristic |
| 34 | C4 | #14555518 | 1 | 1 | yes | characteristic |
| 35 | C2 | — | 2 | 1 | no | — |
| 36 | C2 | #17984155 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 18. C137 | #364 | semidirect |