Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
322 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 121 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 | C22⋊Q8×C107 | C2 |
| hypercenter | C22⋊Q8 | D107 |
| hypocenter | C107 | C2×C22⋊Q8 |
| LCS | G ▷ C22×C107 ▷ C107 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×D107 | C2 | semidirect |
| 3. #16812089 | C2 | semidirect |
| 4. #16812088 | C2 | semidirect |
| 5. #16812087 | C2 | semidirect |
| 6. #16812086 | C2 | semidirect |
| 7. #16812085 | C2 | semidirect |
| 8. C4⋊C4×D107 | C2 | semidirect |
| 9. C4⋊C4×D107 | C2 | semidirect |
| 11. C22⋊Q8×C107 | C2 | semidirect |
| 13. C2×Dic214 | C22 | semidirect |
| 14. C2×Dic214 | C22 | semidirect |
| 24. C4⋊Dic107 | C22 | semidirect |
| 25. C4⋊Dic107 | C22 | semidirect |
| 26. Dic107⋊C4 | C22 | semidirect |
| 27. Dic107⋊C4 | C22 | semidirect |
| 28. Dic107⋊C4 | C22 | semidirect |
| 32. C2×Q8×C107 | C22 | semidirect |
| 34. C4⋊C4×C107 | C22 | semidirect |
| 35. C4⋊C4×C107 | C22 | semidirect |
| 40. C22×D107 | Q8 | semidirect |
| 64. C22×C107 | C2×Q8 | semidirect |
| 71. C2×D107 | C2×Q8 | semidirect |
| 86. D107 | C22⋊Q8 | direct (N × H) |
| 87. C107 | C2×C22⋊Q8 | semidirect |
| 96. C22⋊Q8 | D107 | direct (N × H) |
| 104. C2×Q8 | C2×D107 | semidirect |
| 119. C4⋊C4 | C2×D107 | semidirect |
| 120. C4⋊C4 | C2×D107 | semidirect |
| 159. C22 | Q8×D107 | semidirect |