Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
46 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #19128772 | C2 | 1 | 2 | yes | maximal |
| 2 | #97×C167 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C167⋊C16 | C4 | 1 | 4 | yes | complemented |
| 4 | C2×C8×C167 | C4 | 1 | 1 | yes | characteristic |
| 5 | C2×C8×C167 | C22 | 1 | 1 | yes | characteristic |
| 6 | C42×C167 | C4 | 1 | 1 | yes | characteristic |
| 7 | C2×C4×C167 | — | 2 | 1 | no | — |
| 8 | C2×C4×C167 | C2×C4 | 1 | 1 | yes | characteristic |
| 9 | C8×C167 | — | 2 | 1 | no | — |
| 10 | C8×C167 | C2×C4 | 1 | 2 | yes | — |
| 11 | C22×C167 | M16 | 1 | 1 | yes | characteristic |
| 12 | C4×C167 | — | 4 | 1 | no | — |
| 13 | C4×C167 | C42 | 1 | 1 | yes | characteristic |
| 14 | C4×C167 | M16 | 1 | 1 | yes | characteristic |
| 15 | C2×C167 | — | 2 | 1 | no | — |
| 16 | C2×C167 | #97 | 1 | 1 | yes | characteristic |
| 17 | C167 | #347 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 18 | #347 | — | 167 | 1 | no | maximal, Sylow |
| 19 | M32 | — | 167 | 2 | no | — |
| 20 | #97 | D167 | 1 | 1 | yes | characteristic |
| 21 | C2×C8 | Dic167 | 1 | 1 | yes | characteristic |
| 22 | C2×C8 | C2×D167 | 1 | 1 | yes | characteristic |
| 23 | C42 | Dic167 | 1 | 1 | yes | characteristic |
| 24 | C16 | — | 167 | 4 | no | — |
| 25 | C2×C4 | — | 2 | 1 | no | — |
| 26 | C2×C4 | C2×Dic167 | 1 | 1 | yes | characteristic |
| 27 | C8 | — | 2 | 1 | no | — |
| 28 | C8 | C4×D167 | 1 | 2 | yes | — |
| 29 | C22 | #14581934 | 1 | 1 | yes | characteristic |
| 30 | C4 | — | 4 | 1 | no | — |
| 31 | C4 | C4×Dic167 | 1 | 1 | yes | characteristic |
| 32 | C4 | #14581934 | 1 | 1 | yes | characteristic |
| 33 | C2 | — | 2 | 1 | no | — |
| 34 | C2 | #19128743 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C167⋊C16 | C4 | semidirect |
| 17. C167 | #347 | semidirect |