Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
738 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 1. C2×#14524074 | C2 | semidirect |
| 3. #16863552 | C2 | semidirect |
| 4. #16863535 | C2 | semidirect |
| 5. #16863405 | C2 | semidirect |
| 6. #16863360 | C2 | semidirect |
| 7. C23×Q8×C67 | C2 | semidirect |
| 10. C2×#11761618 | C22 | semidirect |
| 11. C2×#11761615 | C22 | semidirect |
| 19. #14523967 | C22 | semidirect |
| 51. C2×Q8×C67 | D4 | semidirect |
| 93. C22×C67 | #137 | semidirect |
| 109. C67 | #3004 | semidirect |
| 110. C23×Q8 | D67 | semidirect |
| 146. C2×Q8 | C22⋊D67 | semidirect |
| 204. C22 | #14524074 | semidirect |