Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
220 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D107 |
| commutator, socle | C22×C107 | C24 |
| Fitting | #123×C107 | C2 |
| hypercenter | #123 | D107 |
| hypocenter | C107 | #562 |
| LCS | G ▷ C22×C107 ▷ C107 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16812100 | C2 | semidirect |
| 2. #16812095 | C2 | semidirect |
| 3. #16812095 | C2 | semidirect |
| 4. #16812094 | C2 | semidirect |
| 5. #16812093 | C2 | semidirect |
| 6. #16812091 | C2 | semidirect |
| 7. #16812089 | C2 | semidirect |
| 8. #16812088 | C2 | semidirect |
| 9. #16812087 | C2 | semidirect |
| 10. #16812086 | C2 | semidirect |
| 11. #16812083 | C2 | semidirect |
| 12. #16812082 | C2 | semidirect |
| 13. #16812081 | C2 | semidirect |
| 14. #16812080 | C2 | semidirect |
| 15. #123×C107 | C2 | semidirect |
| 109. C107 | #562 | semidirect |
| 117. #123 | D107 | semidirect |