Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
294 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 3. #22577141 | C2 | semidirect |
| 5. C22×Dic274 | C4 | semidirect |
| 8. #17984067 | C4 | semidirect |
| 10. C2×C4⋊Dic137 | C4 | semidirect |
| 94. C137 | #1508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984067 | 2 |
| C4×C22⋊Dic137 | 2 |
| #22577141 | 2 |
| #407×C137 | 2 |
| #1508 | 137 |