Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
924 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 201 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 | C2×#121×C67 | C2 |
| hypercenter | C2×#121 | D67 |
| hypocenter | C67 | #2856 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524039 | C2 | semidirect |
| 2. C2×#14524017 | C2 | semidirect |
| 3. C2×#14524015 | C2 | semidirect |
| 4. C22×C4×Dic67 | C2 | semidirect |
| 5. #16863299 | C2 | semidirect |
| 6. #16863297 | C2 | semidirect |
| 7. #16863296 | C2 | semidirect |
| 8. #16863265 | C2 | semidirect |
| 9. C2×#121×C67 | C2 | semidirect |
| 43. C22×Dic67 | D4 | semidirect |
| 54. C4×Dic67 | D4 | semidirect |
| 64. C22×C4×C67 | D4 | semidirect |
| 118. C22×C67 | #127 | semidirect |
| 131. C4×C67 | #121 | semidirect |
| 134. Dic67 | #121 | semidirect |
| 144. C67 | #2856 | semidirect |
| 148. C2×#121 | D67 | semidirect |
| 200. C22×C4 | C22⋊D67 | semidirect |
| 267. C22 | #14524039 | semidirect |
| 278. C4 | #14524015 | semidirect |