Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
258 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 64 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 | C2×D4×C109 | C4 |
| hypercenter | C2×D4 | #89137 |
| hypocenter | C109 | #390 |
| LCS | G ▷ C22×C109 ▷ C109 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊#89137 | C2 | semidirect |
| 2. C2×C22⋊#89137 | C2 | semidirect |
| 3. C2×C4×#89137 | C2 | semidirect |
| 11. C2×D436 | C4 | semidirect |
| 12. C2×C22⋊D109 | C4 | semidirect |
| 16. C2×D4×C109 | C4 | semidirect |
| 28. C2×#89137 | D4 | semidirect |
| 50. C4×C109 | C22⋊C4 | semidirect |
| 51. Dic109 | C22⋊C4 | semidirect |
| 59. C109 | #390 | semidirect |
| 70. C2×D4 | #89137 | semidirect |
| 111. C4 | C22⋊#89137 | semidirect |