Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
552 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 213 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 | C22×C67 | C23×C4 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | C2×C4⋊C8×C67 | C2 |
| socle | C23×C67 | C22×C4 |
| hypercenter | C2×C4⋊C8 | D67 |
| hypocenter | C67 | C2×#436 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11761611 | C2 | semidirect |
| 3. #16863473 | C2 | direct (N × H) |
| 4. C2×(C2×D67)⋊C8 | C2 | semidirect |
| 5. C2×C4×C67⋊C8 | C2 | semidirect |
| 6. C2×C4⋊C8×C67 | C2 | semidirect |
| 10. C2×#11761611 | C22 | semidirect |
| 17. (C2×D67)⋊C8 | C22 | semidirect |
| 18. C4×C67⋊C8 | C22 | semidirect |
| 21. C4⋊C8×C67 | C22 | semidirect |
| 32. C2×C67⋊C8 | D4 | semidirect |
| 50. C2×C4×C67 | M16 | semidirect |
| 65. C67⋊C8 | C2×D4 | semidirect |
| 76. C4×C67 | C2×M16 | semidirect |
| 80. C2×C67 | #436 | semidirect |
| 86. C67 | C2×#436 | semidirect |
| 90. C2×C4⋊C8 | D67 | semidirect |
| 105. C4⋊C8 | C2×D67 | semidirect |
| 142. C2×C4 | #11761611 | semidirect |
| 163. C4 | C2×#11761611 | semidirect |
| 167. C2 | #16863473 | direct (N × H) |