Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
948 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 948 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 | C2×C4×D4×C67 | C2 |
| hypercenter | C2×C4×D4 | D67 |
| hypocenter | C67 | #2541 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C2×C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524040 | C2 | semidirect |
| 2. C2×#14524039 | C2 | semidirect |
| 3. C2×#14524017 | C2 | semidirect |
| 4. #16863305 | C2 | semidirect |
| 5. #16863297 | C2 | semidirect |
| 6. C4×C4⋊Dic67 | C2 | semidirect |
| 7. C2×C4×D4×C67 | C2 | semidirect |
| 37. C4⋊Dic67 | D4 | semidirect |
| 43. C2×D4×C67 | D4 | semidirect |
| 52. C42×C67 | D4 | semidirect |
| 99. C4×C67 | #121 | semidirect |
| 100. C4×C67 | #127 | semidirect |
| 110. C67 | #2541 | semidirect |
| 114. C2×C4×D4 | D67 | semidirect |
| 149. C2×D4 | D268 | semidirect |
| 162. C42 | C22⋊D67 | semidirect |
| 210. C4 | #14524017 | semidirect |
| 211. C4 | #14524039 | semidirect |