Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
766 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22561008 | C2 | semidirect |
| 3. #22558910 | C2 | semidirect |
| 4. #22558905 | C2 | semidirect |
| 5. #22558825 | C2 | semidirect |
| 6. #22558821 | C2 | semidirect |
| 7. C67×#1466 | C2 | semidirect |
| 229. #1466 | D67 | semidirect |
| 230. C67 | #8458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574061 | 2 |
| #22561008 | 2 |
| #22558910 | 2 |
| #22558905 | 2 |
| #22558825 | 2 |
| #22558821 | 2 |
| C67×#1466 | 2 |
| #8458 | 67 |