Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
106 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8 | C22⋊D107 |
| commutator | C4×C107 | C22×C4 |
| Frattini | C2×C4 | C22×D107 |
| Fitting | #131×C107 | C2 |
| socle | C2×C107 | C4×D4 |
| hypercenter | #131 | D107 |
| hypocenter | C107 | #443 |
| LCS | G ▷ C4×C107 ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16812115 | C2 | semidirect |
| 3. #16812044 | C2 | semidirect |
| 4. #16812036 | C2 | semidirect |
| 5. #16812035 | C2 | semidirect |
| 6. C8×Dic107 | C2 | semidirect |
| 7. #131×C107 | C2 | semidirect |
| 9. #13133808 | C4 | semidirect |
| 10. #13133806 | C4 | semidirect |
| 11. #13133805 | C4 | semidirect |
| 12. #13133803 | C4 | semidirect |
| 51. C107 | #443 | semidirect |
| 55. #131 | D107 | semidirect |