Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
3592 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 3592 conjugacy classes of subgroups — too many to draw. Only its 331 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. C2×#16863558 | C2 | semidirect |
| 2. C2×#16863552 | C2 | semidirect |
| 3. #22565938 | C2 | semidirect |
| 4. #22560149 | C2 | semidirect |
| 5. #22560144 | C2 | semidirect |
| 6. #22560121 | C2 | semidirect |
| 187. C67 | #32887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863558 | 2 |
| C2×#16863552 | 2 |
| #22565938 | 2 |
| #22560149 | 2 |
| #22560144 | 2 |
| #22560121 | 2 |
| C22×2−1+4×C67 | 2 |
| #32887 | 67 |