Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
434 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22571515 | C2 | semidirect |
| 2. #22562121 | C2 | semidirect |
| 3. #22561517 | C2 | semidirect |
| 4. #22558219 | C2 | semidirect |
| 5. #22558218 | C2 | semidirect |
| 6. #22558148 | C2 | semidirect |
| 7. C67×#2184 | C2 | semidirect |
| 149. C2×Dic67 | D16 | semidirect |
| 194. #2184 | D67 | semidirect |
| 199. C67 | #12158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571515 | 2 |
| #22562121 | 2 |
| #22561517 | 2 |
| #22558219 | 2 |
| #22558218 | 2 |
| #22558148 | 2 |
| C67×#2184 | 2 |
| #12158 | 67 |