Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
170 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 52 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×#14555520 | C2 | semidirect |
| 2. C2×C4×#10587739 | C2 | semidirect |
| 3. #17984153 | C2 | direct (N × H) |
| 7. #14555520 | C22 | semidirect |
| 10. C4×#10587739 | C22 | semidirect |
| 13. #14555511 | C4 | semidirect |
| 16. C2×D548 | C4 | semidirect |
| 19. C2×Q8×C137 | C4 | semidirect |
| 28. D548 | C2×C4 | semidirect |
| 37. Q8×C137 | C2×C4 | semidirect |
| 52. C2×C137 | #104 | semidirect |
| 57. C137 | C2×#104 | semidirect |
| 67. C2×Q8 | #10587739 | semidirect |
| 81. Q8 | C2×#10587739 | semidirect |
| 113. C2 | #17984153 | direct (N × H) |