Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D107 |
| commutator, socle | C2×C107 | C23×C4 |
| Fitting | #131×C107 | C2 |
| hypercenter | #131 | D107 |
| hypocenter | C107 | #568 |
| LCS | G ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C4 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16812117 | C2 | semidirect |
| 3. #16812116 | C2 | semidirect |
| 4. #16812115 | C2 | semidirect |
| 5. C2×#13133801 | C2 | semidirect |
| 6. M16×D107 | C2 | semidirect |
| 7. #131×C107 | C2 | semidirect |
| 14. #13133802 | C22 | semidirect |
| 17. #13133801 | C22 | semidirect |
| 18. #13133801 | C22 | semidirect |
| 19. C2×C107⋊C8 | C22 | semidirect |
| 20. C8×D107 | C22 | semidirect |
| 22. M16×C107 | C22 | semidirect |
| 23. C2×C8×C107 | C22 | semidirect |
| 52. C107 | #568 | semidirect |
| 58. #131 | D107 | semidirect |
| 73. M16 | C2×D107 | semidirect |
| 76. C2×C8 | C2×D107 | semidirect |