Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. C2×#17984013 | C2 | semidirect |
| 5. C2×#17984006 | C2 | semidirect |
| 6. #22577171 | C2 | semidirect |
| 7. #341×C137 | C2 | semidirect |
| 11. #17984121 | C4 | semidirect |
| 116. C137 | #1908 | semidirect |
| 124. #341 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984121 | 2 |
| C2×#17984094 | 2 |
| #22577405 | 2 |
| C2×#17984013 | 2 |
| C2×#17984006 | 2 |
| #22577171 | 2 |
| #341×C137 | 2 |
| #1908 | 137 |