Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
294 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 151 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 | C23×D137 |
| commutator | C2×C137 | C23×C4 |
| Fitting | #117×C137 | C2 |
| socle | C22×C137 | C24 |
| hypercenter | #117 | D137 |
| hypocenter | C137 | #520 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×Dic274 | C2 | semidirect |
| 3. C4×D548 | C2 | semidirect |
| 4. #17984048 | C2 | semidirect |
| 5. #17984046 | C2 | semidirect |
| 6. C2×C4⋊Dic137 | C2 | semidirect |
| 7. C4⋊C4×D137 | C2 | semidirect |
| 8. #117×C137 | C2 | semidirect |
| 9. #14555510 | C4 | semidirect |
| 27. Dic274 | C2×C4 | semidirect |
| 28. D548 | C2×C4 | semidirect |
| 29. C22⋊D137 | C2×C4 | semidirect |
| 34. C4×D137 | C2×C4 | semidirect |
| 36. C2×C4×C137 | C2×C4 | semidirect |
| 59. C137 | #520 | semidirect |
| 66. #117 | D137 | semidirect |
| 96. C2×C4 | C4×D137 | semidirect |