Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
1464 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 525 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 | C4×C67 | C25 |
| Frattini | C4 | C24×D67 |
| Fitting | C22×Q16×C67 | C2 |
| socle | C23×C67 | C2×D4 |
| hypercenter | C22×Q16 | D67 |
| hypocenter | C67 | C22×#137 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×Q16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×Q8×D67 | C2 | semidirect |
| 3. C2×#14524075 | C2 | direct (N × H) |
| 4. C22×#11761618 | C2 | semidirect |
| 5. C22×#11761617 | C2 | semidirect |
| 6. C22×#11761615 | C2 | semidirect |
| 7. C22×#11761611 | C2 | semidirect |
| 8. C22×Q16×C67 | C2 | semidirect |
| 14. C2×Q8×D67 | C22 | semidirect |
| 20. #14524075 | C22 | direct (N × H) |
| 21. C2×#11761618 | C22 | semidirect |
| 22. C2×#11761617 | C22 | semidirect |
| 23. C2×#11761615 | C22 | semidirect |
| 24. C2×#11761611 | C22 | semidirect |
| 28. C2×Q16×C67 | C22 | semidirect |
| 38. Q8×D67 | C23 | semidirect |
| 48. #11761618 | C23 | semidirect |
| 49. #11761617 | C23 | semidirect |
| 50. #11761615 | C23 | semidirect |
| 51. #11761611 | C23 | semidirect |
| 60. Q16×C67 | C23 | semidirect |
| 89. C22×C67 | #137 | semidirect |
| 101. C2×C67 | C2×#137 | semidirect |
| 106. C67 | C22×#137 | semidirect |
| 111. C22×Q16 | D67 | semidirect |
| 130. C2×Q16 | C2×D67 | semidirect |
| 162. Q16 | C22×D67 | semidirect |
| 199. C22 | #14524075 | direct (N × H) |
| 209. C2 | C2×#14524075 | direct (N × H) |