Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
344 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22562437 | C2 | semidirect |
| 3. #22562361 | C2 | semidirect |
| 5. #22558257 | C2 | semidirect |
| 7. C67×#1332 | C2 | semidirect |
| 138. #1332 | D67 | semidirect |
| 140. C67 | #12374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×D268 | 2 |
| #22562437 | 2 |
| #22562361 | 2 |
| #22559609 | 2 |
| #22558257 | 2 |
| #22558165 | 2 |
| C67×#1332 | 2 |
| #12374 | 67 |