Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
202 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#11764049 |
| commutator | C2×C137 | C22×C8 |
| Frattini | C2 | C22×#11764049 |
| Fitting | C23×C137 | C8 |
| socle | C22×C137 | C2×C8 |
| hypercenter | C23 | #11764049 |
| hypocenter | C137 | C2×C22⋊C8 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C22 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11764049 | C2 | semidirect |
| 2. C22⋊#11764049 | C2 | direct (N × H) |
| 5. C2×#11764049 | C22 | semidirect |
| 22. C22×D137 | C8 | semidirect |
| 23. C22×D137 | C8 | semidirect |
| 26. C23×C137 | C8 | semidirect |
| 29. C22×C137 | C2×C8 | semidirect |
| 36. C2×D137 | C2×C8 | semidirect |
| 43. C2×C137 | C22⋊C8 | semidirect |
| 46. D137 | C22⋊C8 | semidirect |
| 49. C137 | C2×C22⋊C8 | semidirect |
| 68. C23 | #11764049 | semidirect |
| 88. C22 | C2×#11764049 | semidirect |
| 97. C2 | C22⋊#11764049 | direct (N × H) |