Finite Group DatabasebetaFinite Group DatabasebetaOrder 8384.
342 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D131 |
| commutator | C22×C131 | C24 |
| Frattini | C22 | C23×D131 |
| Fitting | C22×D4×C131 | C2 |
| socle | C23×C131 | C23 |
| hypercenter | C22×D4 | D131 |
| hypocenter | C131 | C2×#123 |
| LCS | G ▷ C22×C131 ▷ C131 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×Dic131 | C2 | semidirect |
| 2. #16862227 | C2 | direct (N × H) |
| 3. C2×Dic131⋊C4 | C2 | semidirect |
| 4. C2×C22⋊Dic131 | C2 | semidirect |
| 5. C2×C22⋊Dic131 | C2 | semidirect |
| 10. C22×Dic131 | C22 | semidirect |
| 11. Dic131⋊C4 | C22 | semidirect |
| 12. C22⋊Dic131 | C22 | semidirect |
| 13. C22⋊Dic131 | C22 | semidirect |
| 48. C2×C131 | #123 | semidirect |
| 51. C131 | C2×#123 | semidirect |
| 100. C2 | #16862227 | direct (N × H) |