Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
948 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 185 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×#127×C67 | C2 |
| hypercenter | C2×#127 | D67 |
| hypocenter | C67 | #2541 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524039 | C2 | semidirect |
| 2. C2×#14524039 | C2 | semidirect |
| 3. C2×#14524015 | C2 | semidirect |
| 4. C2×D4×Dic67 | C2 | semidirect |
| 5. #16863304 | C2 | semidirect |
| 6. #16863299 | C2 | semidirect |
| 7. #16863298 | C2 | semidirect |
| 8. C4×Dic67⋊C4 | C2 | semidirect |
| 9. C2×#127×C67 | C2 | semidirect |
| 50. Dic67⋊C4 | D4 | semidirect |
| 55. C4×Dic67 | D4 | semidirect |
| 66. C2×D4×C67 | D4 | semidirect |
| 130. C4×C67 | #121 | semidirect |
| 134. Dic67 | #127 | semidirect |
| 144. C67 | #2541 | semidirect |
| 147. C2×#127 | D67 | semidirect |
| 197. C2×D4 | C22⋊D67 | semidirect |
| 278. C4 | #14524015 | semidirect |