Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
552 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 185 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. #22577297 | C2 | semidirect |
| 3. #22577297 | C2 | semidirect |
| 4. #22577284 | C2 | semidirect |
| 6. C4×#14555489 | C2 | semidirect |
| 7. C22⋊C4×Dic137 | C2 | semidirect |
| 8. C22⋊C4×Dic137 | C2 | semidirect |
| 12. #17984069 | C4 | semidirect |
| 36. C22×Dic137 | C2×C4 | semidirect |
| 42. #14555489 | C2×C4 | semidirect |
| 46. C22⋊Dic137 | C2×C4 | semidirect |
| 126. C137 | #2374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984069 | 2 |
| #22577297 | 2 |
| #22577284 | 2 |
| #22577283 | 2 |
| C4×#14555489 | 2 |
| C22⋊C4×Dic137 | 2 |
| #390×C137 | 2 |
| #2374 | 137 |