Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 3. #22577300 | C2 | semidirect |
| 4. #22577297 | C2 | semidirect |
| 5. #22577291 | C2 | semidirect |
| 6. #22577285 | C2 | semidirect |
| 7. #22577276 | C2 | semidirect |
| 8. #22577261 | C2 | semidirect |
| 11. #17984069 | C4 | semidirect |
| 34. C22×Dic137 | C2×C4 | semidirect |
| 43. #14555489 | C2×C4 | semidirect |
| 47. C22⋊Dic137 | C2×C4 | semidirect |
| 126. C137 | #2376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984069 | 2 |
| #22577306 | 2 |
| #22577300 | 2 |
| #22577297 | 2 |
| #22577291 | 2 |
| #22577285 | 2 |
| #22577276 | 2 |
| #22577261 | 2 |
| #386×C137 | 2 |
| #2376 | 137 |