Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
258 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 84 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 | C22×#89137 |
| commutator | C2×C109 | C2×C42 |
| Fitting | C22⋊C4×C109 | C4 |
| socle | C22×C109 | C22×C4 |
| hypercenter | C22⋊C4 | #89137 |
| hypocenter | C109 | C4×C22⋊C4 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C4×#89137 | C2 | semidirect |
| 4. (C2×#89137)⋊C4 | C2 | semidirect |
| 7. C22×#89137 | C4 | semidirect |
| 11. C22⋊#89137 | C4 | semidirect |
| 15. C22⋊Dic109 | C4 | semidirect |
| 16. #13182006 | C4 | semidirect |
| 17. C22⋊C4×C109 | C4 | semidirect |
| 31. C2×#89137 | C2×C4 | semidirect |
| 33. C2×C4×C109 | C2×C4 | semidirect |
| 34. C2×Dic109 | C2×C4 | semidirect |
| 38. C22×C109 | C42 | semidirect |
| 44. C2×D109 | C42 | semidirect |
| 51. #89137 | C22⋊C4 | direct (N × H) |
| 61. C109 | C4×C22⋊C4 | semidirect |
| 78. C22⋊C4 | #89137 | direct (N × H) |
| 98. C2×C4 | C2×#89137 | semidirect |
| 109. C22 | C4×#89137 | semidirect |