Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D428 |
| commutator | C4×C107 | C22×C4 |
| Frattini | C2×C4 | C22×D107 |
| Fitting | #97×C107 | C2 |
| socle | C22×C107 | C2×D4 |
| hypercenter | #97 | D107 |
| hypocenter | C107 | #440 |
| LCS | G ▷ C4×C107 ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×Dic214 | C2 | semidirect |
| 4. #16812043 | C2 | semidirect |
| 5. #16812034 | C2 | semidirect |
| 7. #97×C107 | C2 | semidirect |
| 11. #13133807 | C4 | semidirect |
| 31. Dic214 | C2×C4 | semidirect |
| 33. C8×C107 | C2×C4 | semidirect |
| 49. C107 | #440 | semidirect |
| 57. #97 | D107 | semidirect |
| 83. C8 | C4×D107 | semidirect |