Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
106 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | D4×D137 |
| commutator | C4×C137 | C22×C4 |
| Frattini | C2×C4 | C22×D137 |
| Fitting | #104×C137 | C2 |
| socle | C2×C137 | C4×D4 |
| hypercenter | #104 | D137 |
| hypocenter | C137 | #443 |
| LCS | G ▷ C4×C137 ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #104 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17984096 | C2 | semidirect |
| 3. #17984095 | C2 | semidirect |
| 4. #17984023 | C2 | semidirect |
| 5. #17984016 | C2 | semidirect |
| 6. C4×#11764040 | C2 | semidirect |
| 7. #104×C137 | C2 | semidirect |
| 9. #14555500 | C4 | semidirect |
| 10. #14555498 | C4 | semidirect |
| 11. #14555497 | C4 | semidirect |
| 12. #14555495 | C4 | semidirect |
| 51. C137 | #443 | semidirect |
| 58. #104 | D137 | semidirect |