Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
296 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 62 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. #22578280 | C2 | semidirect |
| 10. #17984047 | C4 | semidirect |
| 11. C22⋊C4×D137 | C4 | semidirect |
| 13. #117×C137 | C4 | semidirect |
| 70. C137 | #1828 | semidirect |
| 79. #117 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984147 | 2 |
| #22578280 | 2 |
| #22577877 | 2 |
| #1828 | 137 |