Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
392 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863683 | C2 | semidirect |
| 3. #16863681 | C2 | semidirect |
| 4. #16863627 | C2 | semidirect |
| 5. #16863598 | C2 | semidirect |
| 6. #16863596 | C2 | semidirect |
| 7. C2×C4⋊(C67⋊C8) | C2 | semidirect |
| 8. #533×C67 | C2 | semidirect |
| 74. C2×C4×C67 | SD16 | semidirect |
| 113. C67 | #3246 | semidirect |
| 114. #533 | D67 | semidirect |
| 195. C2×C4 | #11761615 | semidirect |