Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
520 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22569925 | C2 | semidirect |
| 2. C2×#16863203 | C2 | semidirect |
| 3. #22561824 | C2 | semidirect |
| 4. #22558313 | C2 | semidirect |
| 5. C67×#3414 | C2 | semidirect |
| 137. #3414 | D67 | semidirect |
| 142. C67 | #13312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569925 | 2 |
| C2×#16863203 | 2 |
| #22561824 | 2 |
| #22558313 | 2 |
| C67×#3414 | 2 |
| #13312 | 67 |