Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
526 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22560188 | C2 | semidirect |
| 3. #22560188 | C2 | semidirect |
| 4. #22558033 | C2 | semidirect |
| 5. #22558031 | C2 | semidirect |
| 6. #22558030 | C2 | semidirect |
| 7. C67×#1270 | C2 | semidirect |
| 230. #1270 | D67 | semidirect |
| 231. C67 | #7714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568539 | 2 |
| #22560188 | 2 |
| #22558033 | 2 |
| #22558031 | 2 |
| #22558030 | 2 |
| C67×#1270 | 2 |
| #7714 | 67 |