Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
336 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 336 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. #22573299 | C2 | semidirect |
| 2. #22562475 | C2 | semidirect |
| 3. #22562245 | C2 | semidirect |
| 4. #22559693 | C2 | semidirect |
| 5. #22558253 | C2 | semidirect |
| 6. #22558177 | C2 | semidirect |
| 7. C67×#1338 | C2 | semidirect |
| 167. #1338 | D67 | semidirect |
| 169. C67 | #12336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573299 | 2 |
| #22562475 | 2 |
| #22562245 | 2 |
| #22559693 | 2 |
| #22558253 | 2 |
| #22558177 | 2 |
| C67×#1338 | 2 |
| #12336 | 67 |