Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
598 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 1. C22×C22⋊#10587739 | C2 | semidirect |
| 2. C2×#17984146 | C2 | semidirect |
| 3. #22578344 | C2 | semidirect |
| 4. #22578281 | C2 | semidirect |
| 15. C22×C22⋊D137 | C4 | semidirect |
| 21. C2×C22⋊Dic137 | C4 | semidirect |
| 22. C2×#14555487 | C4 | semidirect |
| 24. C22×D4×C137 | C4 | semidirect |
| 36. C22⋊#10587739 | D4 | semidirect |
| 54. C22×Dic137 | C2×C4 | semidirect |
| 55. C22×Dic137 | C2×C4 | semidirect |
| 63. C24×C137 | C2×C4 | semidirect |
| 67. C22×C4×C137 | C2×C4 | semidirect |
| 137. C22×C137 | #99 | semidirect |
| 158. C2×D137 | #99 | semidirect |
| 179. C137 | #1898 | semidirect |
| 189. C22×D4 | #10587739 | semidirect |
| 216. C24 | C2×#10587739 | semidirect |
| 234. C22×C4 | C2×#10587739 | semidirect |
| 339. C22 | #17984146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#10587739 | 2 |
| C2×#17984146 | 2 |
| #22578344 | 2 |
| #22578281 | 2 |
| C2×#17984056 | 2 |
| #1898 | 137 |