Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
298 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 23. #17984013 | C4 | semidirect |
| 24. #17984012 | C4 | semidirect |
| 25. #17984011 | C4 | semidirect |
| 26. #103×C137 | C4 | semidirect |
| 77. Dic274 | C4⋊C4 | semidirect |
| 91. Q8×C137 | C4⋊C4 | semidirect |
| 122. C137 | #1863 | semidirect |
| 148. #103 | #10587739 | semidirect |
| 189. Q8 | C4⋊#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#10587739 | 2 |
| C2×#17984157 | 2 |
| C2×#17984151 | 2 |
| #22578354 | 2 |
| #22578276 | 2 |
| #22578268 | 2 |
| #103×D137 | 2 |
| #1863 | 137 |