Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 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 | #126×C107 | C2 |
| hypercenter | #126 | D107 |
| hypocenter | C107 | #563 |
| LCS | G ▷ C22×C107 ▷ C107 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16812109 | C2 | semidirect |
| 2. #16812108 | C2 | semidirect |
| 3. #16812104 | C2 | semidirect |
| 4. #16812103 | C2 | semidirect |
| 5. #16812102 | C2 | semidirect |
| 6. #16812100 | C2 | semidirect |
| 7. #16812099 | C2 | semidirect |
| 11. #16812089 | C2 | semidirect |
| 12. #16812087 | C2 | semidirect |
| 13. #16812086 | C2 | semidirect |
| 14. #16812086 | C2 | semidirect |
| 15. #126×C107 | C2 | semidirect |
| 97. C107 | #563 | semidirect |
| 104. #126 | D107 | semidirect |