Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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×#16863434 | C2 | semidirect |
| 2. #22562414 | C2 | semidirect |
| 3. #22562397 | C2 | semidirect |
| 4. #22561998 | C2 | semidirect |
| 5. #22561921 | C2 | semidirect |
| 6. #22561820 | C2 | semidirect |
| 14. #16863223 | C22 | semidirect |
| 15. #16863221 | C22 | semidirect |
| 16. #16863200 | C22 | semidirect |
| 17. #16863197 | C22 | semidirect |
| 151. C67 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863434 | 2 |
| #22562414 | 2 |
| #22562397 | 2 |
| #22561998 | 2 |
| #22561921 | 2 |
| #22561820 | 2 |
| C67×#3050 | 2 |
| #33647 | 67 |