Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
40 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #16812045 | C2 | 1 | 2 | yes | maximal |
| 2 | C2×C16×C107 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13133802 | — | 2 | 2 | no | — |
| 4 | C2×C8×C107 | C22 | 1 | 1 | yes | characteristic |
| 5 | C16×C107 | C4 | 1 | 2 | yes | — |
| 6 | C2×C4×C107 | D4 | 1 | 1 | yes | characteristic |
| 7 | C8×C107 | C2×C4 | 1 | 1 | yes | characteristic |
| 8 | C8×C107 | Q8 | 1 | 1 | yes | characteristic |
| 9 | C107⋊C8 | — | 4 | 2 | no | — |
| 10 | C22×C107 | Q16 | 1 | 1 | yes | characteristic |
| 11 | C4×C107 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 12 | C4×C107 | D8 | 1 | 1 | yes | characteristic |
| 13 | C2×C107 | — | 2 | 1 | no | — |
| 14 | C2×C107 | #107 | 1 | 1 | yes | characteristic |
| 15 | C107 | #368 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | #368 | — | 107 | 1 | no | maximal, Sylow |
| 17 | C2×C16 | D107 | 1 | 1 | yes | characteristic |
| 18 | #108 | — | 107 | 2 | no | — |
| 19 | M16 | — | 214 | 2 | no | — |
| 20 | C2×C8 | C2×D107 | 1 | 1 | yes | characteristic |
| 21 | C16 | Dic107 | 1 | 2 | yes | — |
| 22 | C2×C4 | D428 | 1 | 1 | yes | characteristic |
| 23 | C8 | — | 428 | 2 | no | — |
| 24 | C8 | Dic214 | 1 | 1 | yes | characteristic |
| 25 | C8 | C2×Dic107 | 1 | 1 | yes | characteristic |
| 26 | C22 | Dic428 | 1 | 1 | yes | characteristic |
| 27 | C4 | C4⋊Dic107 | 1 | 1 | yes | characteristic |
| 28 | C4 | D856 | 1 | 1 | yes | characteristic |
| 29 | C2 | — | 2 | 1 | no | — |
| 30 | C2 | #16812043 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 15. C107 | #368 | semidirect |