Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#17984086 | C2 | semidirect |
| 4. #22577606 | C2 | direct (N × H) |
| 5. C2×#17984017 | C2 | semidirect |
| 6. C2×#17984013 | C2 | semidirect |
| 7. C2×#17984012 | C2 | semidirect |
| 15. #17984086 | C22 | semidirect |
| 23. #17984017 | C22 | semidirect |
| 24. #17984013 | C22 | semidirect |
| 25. #17984012 | C22 | semidirect |
| 74. C2×Dic137 | SD16 | semidirect |
| 111. Dic137 | C2×SD16 | semidirect |
| 113. C2×C137 | #461 | semidirect |
| 117. C137 | C2×#461 | semidirect |
| 231. C2 | #22577606 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555498 | 2 |
| C2×#17984086 | 2 |
| C2×D4×Dic137 | 2 |
| #22577606 | 2 |
| C2×#17984017 | 2 |
| C2×#17984013 | 2 |
| C2×#17984012 | 2 |
| C22×SD16×C137 | 2 |
| C2×#461 | 137 |