Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
314 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22572816 | C2 | semidirect |
| 2. #22562451 | C2 | semidirect |
| 3. #22562244 | C2 | semidirect |
| 4. #22559689 | C2 | semidirect |
| 5. #22558262 | C2 | semidirect |
| 6. #22558168 | C2 | semidirect |
| 7. C67×#1333 | C2 | semidirect |
| 158. #1333 | 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 |
|---|---|
| #22572816 | 2 |
| #22562451 | 2 |
| #22562244 | 2 |
| #22559689 | 2 |
| #22558262 | 2 |
| #22558168 | 2 |
| C67×#1333 | 2 |
| #12348 | 67 |