Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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 | #124×C107 | C2 |
| hypercenter | #124 | D107 |
| hypocenter | C107 | #529 |
| LCS | G ▷ C22×C107 ▷ C107 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16812102 | C2 | semidirect |
| 2. #16812101 | C2 | semidirect |
| 3. #16812091 | C2 | semidirect |
| 4. #16812085 | C2 | semidirect |
| 6. Q8×Dic107 | C2 | semidirect |
| 7. D4×Dic107 | C2 | semidirect |
| 8. (C22⋊D107)⋊C4 | C2 | semidirect |
| 9. #16812065 | C2 | semidirect |
| 10. C42×D107 | C2 | semidirect |
| 11. #124×C107 | C2 | semidirect |
| 74. C107 | #529 | semidirect |
| 78. #124 | D107 | semidirect |