Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
368 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 191 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. #22578524 | C2 | direct (N × H) |
| 2. C2×#17984185 | C2 | semidirect |
| 3. C2×#17984184 | C2 | semidirect |
| 4. C2×#17984183 | C2 | semidirect |
| 5. C22×#14555522 | C2 | semidirect |
| 7. #17984185 | C22 | semidirect |
| 8. #17984184 | C22 | semidirect |
| 9. #17984183 | C22 | semidirect |
| 13. C2×#14555522 | C22 | semidirect |
| 66. C2×C137 | #504 | semidirect |
| 69. C137 | C2×#504 | semidirect |
| 137. C2 | #22578524 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578524 | 2 |
| C2×#17984185 | 2 |
| C2×#17984184 | 2 |
| C2×#17984183 | 2 |
| C22×#14555522 | 2 |
| C2×#17984175 | 2 |
| C2×#504 | 137 |