Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 332 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 | C4 | #14524015 |
| commutator | C2×C4×C67 | C22×C4 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | #575×C67 | C2 |
| socle | C2×C67 | #386 |
| hypercenter | #575 | D67 |
| hypocenter | C67 | #1906 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #575 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #41×Dic67 | C2 | semidirect |
| 2. #16863413 | C2 | semidirect |
| 3. C2×#14523970 | C2 | semidirect |
| 4. #16863370 | C2 | semidirect |
| 5. #16863168 | C2 | semidirect |
| 6. #16863157 | C2 | semidirect |
| 24. #137×C67 | C4 | semidirect |
| 26. AGL(1,ℤ/8)×C67 | C4 | semidirect |
| 54. C2×Q8×C67 | C2×C4 | semidirect |
| 58. C2×D4×C67 | C2×C4 | semidirect |
| 68. M16×C67 | C2×C4 | semidirect |
| 130. C67 | #1906 | semidirect |
| 141. #137 | Dic67 | semidirect |
| 143. AGL(1,ℤ/8) | Dic67 | semidirect |
| 167. C2×Q8 | C2×Dic67 | semidirect |
| 171. C2×D4 | C2×Dic67 | semidirect |
| 185. M16 | C2×Dic67 | semidirect |