Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D67 |
| commutator | C22×C4×C67 | C23 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | #340×C67 | C2 |
| socle | C23×C67 | C2×D4 |
| hypercenter | #340 | D67 |
| hypocenter | C67 | #2000 |
| LCS | G ▷ C22×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11761617 | C2 | semidirect |
| 2. C2×#14524023 | C2 | semidirect |
| 4. C2×#14523966 | C2 | semidirect |
| 5. C2×#14523963 | C2 | semidirect |
| 6. C2×(C2×D67)⋊C8 | C2 | semidirect |
| 7. #340×C67 | C2 | semidirect |
| 36. C2×Dic134 | D4 | semidirect |
| 66. C2×C8×C67 | D4 | semidirect |
| 70. C4⋊C4×C67 | D4 | semidirect |
| 85. C22×D67 | SD16 | semidirect |
| 158. C67 | #2000 | semidirect |
| 165. #340 | D67 | semidirect |
| 221. C2×C8 | D268 | semidirect |
| 226. C4⋊C4 | D268 | semidirect |