Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
336 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 2. #22562381 | C2 | semidirect |
| 3. #22562380 | C2 | semidirect |
| 4. #22559842 | C2 | semidirect |
| 5. #22558247 | C2 | semidirect |
| 6. #22558186 | C2 | semidirect |
| 7. C67×#1336 | C2 | semidirect |
| 168. #1336 | D67 | semidirect |
| 169. C67 | #12367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22572014 | 2 |
| #22562381 | 2 |
| #22562380 | 2 |
| #22559842 | 2 |
| #22558247 | 2 |
| #22558186 | 2 |
| C67×#1336 | 2 |
| #12367 | 67 |