Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 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 |
|---|---|---|
| 2. #22577303 | C2 | semidirect |
| 3. #22577295 | C2 | semidirect |
| 4. #22577286 | C2 | semidirect |
| 5. #22577281 | C2 | semidirect |
| 6. #22577279 | C2 | semidirect |
| 7. #22577277 | C2 | semidirect |
| 8. #22577263 | C2 | semidirect |
| 9. #381×C137 | C2 | semidirect |
| 13. #17984062 | C4 | semidirect |
| 37. C2×C22⋊D137 | C2×C4 | semidirect |
| 45. C4⋊Dic137 | C2×C4 | semidirect |
| 52. #14555487 | C2×C4 | semidirect |
| 56. C22×C4×C137 | C2×C4 | semidirect |
| 129. C137 | #2377 | semidirect |
| 138. #381 | D137 | semidirect |
| 176. C22×C4 | C4×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984062 | 2 |
| #22577303 | 2 |
| #22577295 | 2 |
| #22577286 | 2 |
| #22577281 | 2 |
| #22577279 | 2 |
| #22577277 | 2 |
| #22577263 | 2 |
| #381×C137 | 2 |
| #2377 | 137 |