Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
622 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22571124 | C2 | semidirect |
| 2. C2×#16863786 | C2 | semidirect |
| 3. #22558922 | C2 | semidirect |
| 4. #22558820 | C2 | semidirect |
| 5. #22558561 | C2 | semidirect |
| 6. #22558107 | C2 | semidirect |
| 7. C67×#3213 | C2 | semidirect |
| 202. #3213 | D67 | semidirect |
| 209. C67 | #10128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571124 | 2 |
| C2×#16863786 | 2 |
| #22558922 | 2 |
| #22558820 | 2 |
| #22558561 | 2 |
| #22558107 | 2 |
| C67×#3213 | 2 |
| #10128 | 67 |