Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
330 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×#89137 |
| commutator | C2×C109 | C2×C42 |
| Frattini | C22 | C22×#89137 |
| Fitting | C22×C4×C109 | C4 |
| socle | C23×C109 | C2×C4 |
| hypercenter | C22×C4 | #89137 |
| hypocenter | C109 | C2×#95 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. (C2×#89137)⋊C4 | C2 | direct (N × H) |
| 6. C22×#89137 | C4 | semidirect |
| 9. C22×Dic109 | C4 | semidirect |
| 11. C2×C4×D109 | C4 | semidirect |
| 13. C22×C4×C109 | C4 | semidirect |
| 24. C2×#89137 | C2×C4 | semidirect |
| 26. C2×C4×C109 | C2×C4 | semidirect |
| 28. C2×Dic109 | C2×C4 | semidirect |
| 47. C2×C109 | #95 | semidirect |
| 51. D109 | #95 | semidirect |
| 54. C109 | C2×#95 | semidirect |
| 68. C22×C4 | #89137 | semidirect |
| 85. C2×C4 | C2×#89137 | semidirect |
| 105. C2 | (C2×#89137)⋊C4 | direct (N × H) |