Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
480 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 145 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×#17984086 | C2 | semidirect |
| 4. #22577611 | C2 | semidirect |
| 5. #22577606 | C2 | semidirect |
| 6. #22577426 | C2 | semidirect |
| 7. #22577413 | C2 | semidirect |
| 8. #22577412 | C2 | semidirect |
| 116. Dic137 | #137 | semidirect |
| 121. C137 | #3039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984118 | 2 |
| C2×#17984086 | 2 |
| #41×Dic137 | 2 |
| #22577611 | 2 |
| #22577606 | 2 |
| #22577426 | 2 |
| #22577413 | 2 |
| #22577412 | 2 |
| C2×#137×C137 | 2 |
| #3039 | 137 |