Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D107 |
| commutator, socle | C22×C107 | C24 |
| Frattini | C22 | C23×D107 |
| Fitting | C4×D4×C107 | C2 |
| hypercenter | C4×D4 | D107 |
| hypocenter | C107 | #525 |
| LCS | G ▷ C22×C107 ▷ C107 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133818 | C2 | semidirect |
| 2. C22×C4×D107 | C2 | semidirect |
| 3. #16812094 | C2 | semidirect |
| 4. #16812091 | C2 | semidirect |
| 5. #16812087 | C2 | semidirect |
| 6. #16812086 | C2 | semidirect |
| 7. #16812082 | C2 | semidirect |
| 8. #16812081 | C2 | semidirect |
| 9. #16812079 | C2 | semidirect |
| 10. #16812077 | C2 | semidirect |
| 11. C4×D428 | C2 | semidirect |
| 12. C4×C22⋊D107 | C2 | semidirect |
| 13. C4×C22⋊D107 | C2 | semidirect |
| 14. #16812066 | C2 | semidirect |
| 15. C4×D4×C107 | C2 | semidirect |
| 18. C2×Dic214 | C22 | semidirect |
| 24. C2×C22⋊D107 | C22 | semidirect |
| 31. C2×C4×D107 | C22 | semidirect |
| 32. C4⋊Dic107 | C22 | semidirect |
| 33. Dic107⋊C4 | C22 | semidirect |
| 34. Dic107⋊C4 | C22 | semidirect |
| 35. Dic107⋊C4 | C22 | semidirect |
| 36. Dic107⋊C4 | C22 | semidirect |
| 38. C22⋊Dic107 | C22 | semidirect |
| 43. (C2×D107)⋊C4 | C22 | semidirect |
| 44. (C2×D107)⋊C4 | C22 | semidirect |
| 45. C4×Dic107 | C22 | semidirect |
| 48. C22×C4×C107 | C22 | semidirect |
| 49. C4⋊C4×C107 | C22 | semidirect |
| 51. C22⋊C4×C107 | C22 | semidirect |
| 52. C42×C107 | C22 | semidirect |
| 85. C4×D107 | D4 | semidirect |
| 92. C22×C107 | #41 | semidirect |
| 103. C2×D107 | #41 | semidirect |
| 122. C107 | #525 | semidirect |
| 137. C4×D4 | D107 | semidirect |
| 157. C22×C4 | C2×D107 | semidirect |
| 163. C4⋊C4 | C2×D107 | semidirect |
| 173. C22⋊C4 | C2×D107 | semidirect |
| 175. C42 | C2×D107 | semidirect |
| 225. C22 | #13133818 | semidirect |