Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D4×D137 |
| commutator | C4×C137 | C24 |
| Frattini | C4 | C23×D137 |
| Fitting | #137×C137 | C2 |
| socle | C2×C137 | C22×D4 |
| hypercenter | #137 | D137 |
| hypocenter | C137 | #578 |
| LCS | G ▷ C4×C137 ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #137 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17984136 | C2 | semidirect |
| 2. #17984135 | C2 | semidirect |
| 3. #17984121 | C2 | semidirect |
| 4. #17984120 | C2 | semidirect |
| 5. #17984117 | C2 | semidirect |
| 6. #17984109 | C2 | semidirect |
| 7. #17984108 | C2 | semidirect |
| 8. C2×#14555500 | C2 | semidirect |
| 9. Q16×D137 | C2 | semidirect |
| 10. #17984096 | C2 | semidirect |
| 11. #137×C137 | C2 | semidirect |
| 87. C137 | #578 | semidirect |
| 94. #137 | D137 | semidirect |