Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 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. #22577310 | C2 | semidirect |
| 3. #22577295 | C2 | semidirect |
| 4. #22577293 | C2 | semidirect |
| 6. C4×#14555487 | C2 | semidirect |
| 7. #22577250 | C2 | semidirect |
| 8. #22577248 | C2 | semidirect |
| 9. #391×C137 | C2 | semidirect |
| 12. #17984077 | C4 | semidirect |
| 46. #14555487 | C2×C4 | semidirect |
| 47. #14555487 | C2×C4 | semidirect |
| 51. C4×Dic137 | C2×C4 | semidirect |
| 54. C2×Q8×C137 | C2×C4 | semidirect |
| 123. C137 | #2372 | semidirect |
| 127. #391 | D137 | semidirect |
| 159. C2×Q8 | C4×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984077 | 2 |
| #22577310 | 2 |
| #22577295 | 2 |
| #22577293 | 2 |
| #22577281 | 2 |
| C4×#14555487 | 2 |
| #22577250 | 2 |
| #22577248 | 2 |
| #391×C137 | 2 |
| #2372 | 137 |