Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
190 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 54 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, socle | C22×C109 | C22×C4 |
| Fitting | C22⋊C4×C109 | C4 |
| hypercenter | C22⋊C4 | #89137 |
| hypocenter | C109 | #388 |
| LCS | G ▷ C22×C109 ▷ C109 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊#89137 | C2 | semidirect |
| 4. C2×C4×#89137 | C2 | semidirect |
| 5. (C2×#89137)⋊C4 | C2 | semidirect |
| 6. (C2×#89137)⋊C4 | C2 | semidirect |
| 19. C22⋊Dic109 | C4 | semidirect |
| 20. #13182006 | C4 | semidirect |
| 21. #13182006 | C4 | semidirect |
| 22. C22⋊C4×C109 | C4 | semidirect |
| 86. C109 | #388 | semidirect |
| 108. C22⋊C4 | #89137 | semidirect |