Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
704 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 233 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. #22577299 | C2 | semidirect |
| 4. #22577277 | C2 | semidirect |
| 5. #22577262 | C2 | semidirect |
| 6. C4×C4⋊Dic137 | C2 | semidirect |
| 7. #95×D137 | C2 | semidirect |
| 8. #382×C137 | C2 | semidirect |
| 12. C4×D548 | C4 | semidirect |
| 38. C2×C4×D137 | C2×C4 | semidirect |
| 40. C4⋊Dic137 | C2×C4 | semidirect |
| 43. #14555487 | C2×C4 | semidirect |
| 50. C42×C137 | C2×C4 | semidirect |
| 56. D548 | C4⋊C4 | semidirect |
| 101. C137 | #2349 | semidirect |
| 107. #382 | D137 | semidirect |
| 152. C42 | C4×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D548 | 2 |
| C2×#17984050 | 2 |
| #22577299 | 2 |
| #22577277 | 2 |
| #22577262 | 2 |
| C4×C4⋊Dic137 | 2 |
| #95×D137 | 2 |
| #382×C137 | 2 |
| #2349 | 137 |