Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
1360 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 365 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. C22×#14555487 | C2 | semidirect |
| 3. C22×C4×Dic137 | C2 | semidirect |
| 4. #22577304 | C2 | direct (N × H) |
| 5. C22×C4⋊C4×C137 | C2 | semidirect |
| 9. C22×D548 | C4 | semidirect |
| 13. C2×#14555487 | C22 | semidirect |
| 15. C2×C4×Dic137 | C22 | semidirect |
| 19. C2×C4⋊C4×C137 | C22 | semidirect |
| 29. C2×D548 | C2×C4 | semidirect |
| 32. C22×Dic137 | D4 | semidirect |
| 59. C2×Dic137 | C2×D4 | semidirect |
| 69. C2×C4×C137 | C22⋊C4 | semidirect |
| 90. C4×C137 | C2×C22⋊C4 | semidirect |
| 92. C2×C137 | #390 | semidirect |
| 99. C137 | C2×#390 | semidirect |
| 102. C22×C4⋊C4 | D137 | semidirect |
| 115. C2×C4⋊C4 | C2×D137 | semidirect |
| 169. C2×C4 | #14555487 | semidirect |
| 191. C4 | C2×#14555487 | semidirect |
| 193. C2 | #22577304 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D548 | 2 |
| C22×#14555487 | 2 |
| C22×C4×Dic137 | 2 |
| #22577304 | 2 |
| C22×C4⋊C4×C137 | 2 |
| C2×#390 | 137 |