Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
1232 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 189 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 | #380×C67 | C2 |
| hypercenter | #380 | D67 |
| hypocenter | C67 | #2408 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D268 | C2 | semidirect |
| 2. C2×#14524018 | C2 | semidirect |
| 3. C2×#14524013 | C2 | semidirect |
| 4. C2×C4×C22⋊D67 | C2 | semidirect |
| 5. #16863314 | C2 | semidirect |
| 6. #16863306 | C2 | semidirect |
| 7. #16863297 | C2 | semidirect |
| 8. #16863251 | C2 | semidirect |
| 9. #380×C67 | C2 | semidirect |
| 15. C22×D268 | C22 | semidirect |
| 17. C22×C4×D67 | C22 | semidirect |
| 21. C2×Dic67⋊C4 | C22 | semidirect |
| 23. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 24. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 25. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 26. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 27. C2×C4×Dic67 | C22 | semidirect |
| 29. C2×C4⋊C4×C67 | C22 | semidirect |
| 31. #95×C67 | C22 | semidirect |
| 47. C2×D268 | D4 | semidirect |
| 50. C2×C22⋊D67 | D4 | semidirect |
| 65. C22×C4×C67 | D4 | semidirect |
| 93. C22×D67 | C2×D4 | semidirect |
| 109. C2×Dic67 | C2×D4 | semidirect |
| 118. C22×C67 | #121 | semidirect |
| 139. C4×C67 | #120 | semidirect |
| 152. C67 | #2408 | semidirect |
| 160. #380 | D67 | semidirect |
| 175. C2×C4⋊C4 | C2×D67 | semidirect |
| 183. #95 | C2×D67 | semidirect |
| 210. C22×C4 | D268 | semidirect |
| 283. C22 | #14524018 | semidirect |
| 294. C4 | #14524013 | semidirect |