Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
408 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 1. C2×#17984147 | C2 | semidirect |
| 2. #22578345 | C2 | semidirect |
| 3. C4×C22⋊#10587739 | C2 | semidirect |
| 12. C22×D548 | C4 | semidirect |
| 19. C2×#14555487 | C4 | semidirect |
| 20. C2×C4⋊C4×C137 | C4 | semidirect |
| 26. C22⋊#10587739 | D4 | semidirect |
| 104. C4×C137 | #99 | semidirect |
| 115. C137 | #1964 | semidirect |
| 129. C2×C4⋊C4 | #10587739 | semidirect |
| 222. C4 | #17984147 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984147 | 2 |
| #22578345 | 2 |
| C4×C22⋊#10587739 | 2 |
| C2×#17984063 | 2 |
| #1964 | 137 |