Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
1504 conjugacy classes of subgroups; only the 821 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 821 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D67 |
| commutator | C2×C67 | C24×C4 |
| Frattini | C4 | C24×D67 |
| Fitting | C22×M16×C67 | C2 |
| socle | C23×C67 | C22×C4 |
| hypercenter | C22×M16 | D67 |
| hypocenter | C67 | C22×#131 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ C22×M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14524051 | C2 | direct (N × H) |
| 3. C22×#11761611 | C2 | semidirect |
| 4. C23×C67⋊C8 | C2 | semidirect |
| 5. C22×C8×D67 | C2 | semidirect |
| 6. C22×M16×C67 | C2 | semidirect |
| 13. #14524051 | C22 | direct (N × H) |
| 14. C2×#11761611 | C22 | semidirect |
| 17. C22×C67⋊C8 | C22 | semidirect |
| 18. C2×C8×D67 | C22 | semidirect |
| 20. C2×M16×C67 | C22 | semidirect |
| 31. #11761611 | C23 | semidirect |
| 34. C2×C67⋊C8 | C23 | semidirect |
| 35. C8×D67 | C23 | semidirect |
| 41. M16×C67 | C23 | semidirect |
| 63. C22×C67 | #131 | semidirect |
| 73. C2×C67 | C2×#131 | semidirect |
| 77. C67 | C22×#131 | semidirect |
| 81. C22×M16 | D67 | semidirect |
| 93. C2×M16 | C2×D67 | semidirect |
| 114. M16 | C22×D67 | semidirect |
| 142. C22 | #14524051 | direct (N × H) |
| 151. C2 | C2×#14524051 | direct (N × H) |