Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
908 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 203 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 | #396×C67 | C2 |
| hypercenter | #396 | D67 |
| hypocenter | C67 | C2×#396 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #396 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊C4×D67 | C2 | semidirect |
| 3. #16863320 | C2 | semidirect |
| 4. #16863319 | C2 | semidirect |
| 5. #16863318 | C2 | semidirect |
| 6. #95×D67 | C2 | semidirect |
| 7. #396×C67 | C2 | semidirect |
| 11. C2×C4⋊Dic67 | C22 | semidirect |
| 12. C2×Dic67⋊C4 | C22 | semidirect |
| 13. C2×Dic67⋊C4 | C22 | semidirect |
| 19. C67⋊#95 | C22 | semidirect |
| 20. C2×C4⋊C4×C67 | C22 | semidirect |
| 22. #95×C67 | C22 | semidirect |
| 96. D67 | #396 | direct (N × H) |
| 98. C67 | C2×#396 | semidirect |
| 104. #396 | D67 | direct (N × H) |
| 113. C2×C4⋊C4 | C2×D67 | semidirect |
| 120. #95 | C2×D67 | semidirect |