Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D107 |
| commutator | C22×C107 | C24 |
| Frattini | C22 | C23×D107 |
| Fitting | C2×C4⋊C4×C107 | C2 |
| socle | C23×C107 | C23 |
| hypercenter | C2×C4⋊C4 | D107 |
| hypocenter | C107 | C2×C22⋊Q8 |
| LCS | G ▷ C22×C107 ▷ C107 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Dic214 | C2 | semidirect |
| 3. #16812089 | C2 | direct (N × H) |
| 4. C2×C4⋊Dic107 | C2 | semidirect |
| 6. C2×C4⋊C4×C107 | C2 | semidirect |
| 9. C2×Dic214 | C22 | semidirect |
| 14. C4⋊Dic107 | C22 | semidirect |
| 18. C4⋊C4×C107 | C22 | semidirect |
| 22. C22×D107 | Q8 | semidirect |
| 41. C2×D107 | C2×Q8 | semidirect |
| 46. C2×C107 | C22⋊Q8 | semidirect |
| 51. C107 | C2×C22⋊Q8 | semidirect |
| 57. C2×C4⋊C4 | D107 | semidirect |
| 69. C4⋊C4 | C2×D107 | semidirect |
| 99. C2 | #16812089 | direct (N × H) |