Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
286 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 286 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 | #386 |
| 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. C23×#89137 | C2 | semidirect |
| 2. C2×C22⋊#89137 | C2 | semidirect |
| 3. C2×C22⋊#89137 | C2 | semidirect |
| 4. (C2×#89137)⋊C4 | C2 | semidirect |
| 14. C2×D436 | C4 | semidirect |
| 15. C2×C22⋊D109 | C4 | semidirect |
| 16. C2×C22⋊D109 | C4 | semidirect |
| 20. C2×D4×C109 | C4 | semidirect |
| 22. C23×C109 | C2×C4 | semidirect |
| 30. C22×D109 | C2×C4 | semidirect |
| 40. C2×#89137 | D4 | semidirect |
| 42. C2×C4×C109 | C2×C4 | semidirect |
| 45. C2×Dic109 | C2×C4 | semidirect |
| 52. C22×C109 | C22⋊C4 | semidirect |
| 63. C2×D109 | C22⋊C4 | semidirect |
| 81. C109 | #386 | semidirect |
| 95. C2×D4 | #89137 | semidirect |
| 115. C23 | C2×#89137 | semidirect |
| 130. C2×C4 | C2×#89137 | semidirect |
| 148. C22 | C22⋊#89137 | semidirect |