Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22577747 | C2 | semidirect |
| 4. #22577746 | C2 | semidirect |
| 5. #22577740 | C2 | semidirect |
| 6. #22577735 | C2 | semidirect |
| 7. #22577446 | C2 | semidirect |
| 8. #22577411 | C2 | semidirect |
| 9. C2×#17984013 | C2 | semidirect |
| 11. #427×C137 | C2 | semidirect |
| 126. C137 | #3097 | semidirect |
| 135. #427 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577979 | 2 |
| #22577883 | 2 |
| #22577747 | 2 |
| #22577746 | 2 |
| #22577740 | 2 |
| #22577735 | 2 |
| #22577446 | 2 |
| #22577411 | 2 |
| C2×#17984013 | 2 |
| #22577369 | 2 |
| #427×C137 | 2 |
| #3097 | 137 |