Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
314 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 314 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. #22572814 | C2 | semidirect |
| 2. #22562450 | C2 | semidirect |
| 3. #22562241 | C2 | semidirect |
| 4. #22558262 | C2 | semidirect |
| 5. #22558175 | C2 | semidirect |
| 6. #22558167 | C2 | semidirect |
| 7. C67×#1687 | C2 | semidirect |
| 156. #1687 | D67 | semidirect |
| 160. C67 | #12348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22572814 | 2 |
| #22562450 | 2 |
| #22562241 | 2 |
| #22558262 | 2 |
| #22558175 | 2 |
| #22558167 | 2 |
| C67×#1687 | 2 |
| #12348 | 67 |