Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
278 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22560334 | C2 | semidirect |
| 4. #22558311 | C2 | semidirect |
| 5. #22558306 | C2 | semidirect |
| 6. #22558299 | C2 | semidirect |
| 144. C67 | #13489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561916 | 2 |
| #22561108 | 2 |
| #22560334 | 2 |
| #22558311 | 2 |
| #22558306 | 2 |
| #22558299 | 2 |
| C67×#2148 | 2 |
| #13489 | 67 |