Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
708 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D67 |
| commutator, socle | C23×C67 | C24 |
| Fitting | C4×C22⋊C4×C67 | C2 |
| hypercenter | C4×C22⋊C4 | D67 |
| hypocenter | C67 | #2501 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524027 | C2 | semidirect |
| 3. C22×C4⋊Dic67 | C2 | semidirect |
| 4. #16863333 | C2 | semidirect |
| 5. #16863298 | C2 | semidirect |
| 6. #16863266 | C2 | semidirect |
| 7. C4×C22⋊C4×C67 | C2 | semidirect |
| 45. C22⋊C4×C67 | D4 | semidirect |
| 85. C4×C67 | #123 | semidirect |
| 95. C67 | #2501 | semidirect |
| 102. C4×C22⋊C4 | D67 | semidirect |
| 140. C22⋊C4 | D268 | semidirect |
| 182. C4 | #14524027 | semidirect |