Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
310 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D137 |
| commutator, socle | C22×C137 | C24 |
| Frattini | C22 | C23×D137 |
| Fitting | C4×D4×C137 | C2 |
| hypercenter | C4×D4 | D137 |
| hypocenter | C137 | #532 |
| LCS | G ▷ C22×C137 ▷ C137 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14555510 | C2 | semidirect |
| 2. #17984087 | C2 | semidirect |
| 3. #17984084 | C2 | semidirect |
| 4. #17984074 | C2 | semidirect |
| 5. #17984063 | C2 | semidirect |
| 6. #17984061 | C2 | semidirect |
| 7. #17984059 | C2 | semidirect |
| 8. C4×D548 | C2 | semidirect |
| 9. C4×C22⋊D137 | C2 | semidirect |
| 10. C42×D137 | C2 | semidirect |
| 11. C4×D4×C137 | C2 | semidirect |
| 51. C4×D137 | D4 | semidirect |
| 72. C4×C137 | #41 | semidirect |
| 76. Dic137 | #41 | semidirect |
| 83. C137 | #532 | semidirect |
| 94. C4×D4 | D137 | semidirect |
| 160. C4 | #14555510 | semidirect |