Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
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×#10587739 |
| commutator, socle | C22×C137 | C22×C4 |
| Fitting | C2×D4×C137 | C4 |
| hypercenter | C2×D4 | #10587739 |
| hypocenter | C137 | #390 |
| LCS | G ▷ C22×C137 ▷ C137 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊#10587739 | C2 | semidirect |
| 2. C2×C22⋊#10587739 | C2 | semidirect |
| 3. C2×C4×#10587739 | C2 | semidirect |
| 11. C2×D548 | C4 | semidirect |
| 12. C2×C22⋊D137 | C4 | semidirect |
| 16. C2×D4×C137 | C4 | semidirect |
| 21. C2×#10587739 | D4 | semidirect |
| 50. C4×C137 | C22⋊C4 | semidirect |
| 51. Dic137 | C22⋊C4 | semidirect |
| 59. C137 | #390 | semidirect |
| 70. C2×D4 | #10587739 | semidirect |
| 111. C4 | C22⋊#10587739 | semidirect |