Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
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×#10587739 |
| commutator, socle | C22×C137 | C22×C4 |
| Fitting | C2×D4×C137 | C4 |
| hypercenter | C2×D4 | #10587739 |
| hypocenter | C137 | #386 |
| 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. C23×#10587739 | C2 | semidirect |
| 2. C2×C22⋊#10587739 | C2 | semidirect |
| 3. C2×C22⋊#10587739 | C2 | semidirect |
| 4. (C2×#10587739)⋊C4 | C2 | semidirect |
| 14. C2×D548 | C4 | semidirect |
| 15. C2×C22⋊D137 | C4 | semidirect |
| 16. C2×C22⋊D137 | C4 | semidirect |
| 20. C2×D4×C137 | C4 | semidirect |
| 27. C2×#10587739 | D4 | semidirect |
| 35. C22×D137 | C2×C4 | semidirect |
| 42. C2×Dic137 | C2×C4 | semidirect |
| 46. C23×C137 | C2×C4 | semidirect |
| 48. C2×C4×C137 | C2×C4 | semidirect |
| 52. C22×C137 | C22⋊C4 | semidirect |
| 63. C2×D137 | C22⋊C4 | semidirect |
| 81. C137 | #386 | semidirect |
| 95. C2×D4 | #10587739 | semidirect |
| 115. C23 | C2×#10587739 | semidirect |
| 130. C2×C4 | C2×#10587739 | semidirect |
| 148. C22 | C22⋊#10587739 | semidirect |