Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
258 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 84 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×#10587739 |
| commutator | C2×C137 | C2×C42 |
| Fitting | C22⋊C4×C137 | C4 |
| socle | C22×C137 | C22×C4 |
| hypercenter | C22⋊C4 | #10587739 |
| hypocenter | C137 | C4×C22⋊C4 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C4×#10587739 | C2 | semidirect |
| 4. (C2×#10587739)⋊C4 | C2 | semidirect |
| 7. C22×#10587739 | C4 | semidirect |
| 11. C22⋊#10587739 | C4 | semidirect |
| 15. C22⋊Dic137 | C4 | semidirect |
| 16. #14555487 | C4 | semidirect |
| 17. C22⋊C4×C137 | C4 | semidirect |
| 24. C2×#10587739 | C2×C4 | semidirect |
| 32. C2×Dic137 | C2×C4 | semidirect |
| 36. C2×C4×C137 | C2×C4 | semidirect |
| 38. C22×C137 | C42 | semidirect |
| 44. C2×D137 | C42 | semidirect |
| 51. #10587739 | C22⋊C4 | direct (N × H) |
| 61. C137 | C4×C22⋊C4 | semidirect |
| 78. C22⋊C4 | #10587739 | direct (N × H) |
| 98. C2×C4 | C2×#10587739 | semidirect |
| 109. C22 | C4×#10587739 | semidirect |