Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
784 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 210 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. (C2×#10587739)⋊Q8 | C2 | semidirect |
| 10. C22×Dic274 | C4 | semidirect |
| 11. C22×Dic274 | C4 | semidirect |
| 13. C2×Q8×D137 | C4 | semidirect |
| 17. C22×Q8×C137 | C4 | semidirect |
| 83. C137 | #2310 | semidirect |
| 94. C22×Q8 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984167 | 2 |
| (C2×#10587739)⋊Q8 | 2 |
| #22578346 | 2 |
| C22×Q8×D137 | 2 |
| #2310 | 137 |