Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
684 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 320 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 |
|---|---|---|
| 6. Q8×#10587739 | C4 | direct (N × H) |
| 14. Q8×Dic137 | C4 | semidirect |
| 15. C4×Dic274 | C4 | semidirect |
| 16. #17984053 | C4 | semidirect |
| 19. C4×Q8×C137 | C4 | semidirect |
| 26. C4×#10587739 | Q8 | direct (N × H) |
| 47. Dic274 | C42 | semidirect |
| 55. Q8×C137 | C42 | semidirect |
| 65. #10587739 | C4×Q8 | direct (N × H) |
| 68. C4×C137 | C4×Q8 | semidirect |
| 71. Dic137 | C4×Q8 | semidirect |
| 77. C137 | C42×Q8 | semidirect |
| 89. C4×Q8 | #10587739 | direct (N × H) |
| 120. Q8 | C4×#10587739 | direct (N × H) |
| 149. C4 | Q8×#10587739 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#10587739 | 2 |
| C4⋊C4×#10587739 | 2 |
| C4×C4⋊#10587739 | 2 |
| C42×#10587739 | 2 |
| C4×Q8×D137 | 2 |
| C42×Q8 | 137 |