Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 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 | C22×C67 | C23×C4 |
| Fitting | #391×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | #391 | D67 |
| hypocenter | C67 | #2372 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863303 | C2 | semidirect |
| 3. #16863288 | C2 | semidirect |
| 4. #16863286 | C2 | semidirect |
| 6. C4×(C2×D67)⋊C4 | C2 | semidirect |
| 7. #16863243 | C2 | semidirect |
| 8. #16863241 | C2 | semidirect |
| 9. #391×C67 | C2 | semidirect |
| 12. #14524032 | C4 | semidirect |
| 46. (C2×D67)⋊C4 | C2×C4 | semidirect |
| 47. (C2×D67)⋊C4 | C2×C4 | semidirect |
| 51. C4×Dic67 | C2×C4 | semidirect |
| 54. C2×Q8×C67 | C2×C4 | semidirect |
| 124. C67 | #2372 | semidirect |
| 127. #391 | D67 | semidirect |
| 159. C2×Q8 | C4×D67 | semidirect |