Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
498 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22571330 | C2 | semidirect |
| 3. #22570605 | C2 | semidirect |
| 4. #22558800 | C2 | semidirect |
| 5. #22558627 | C2 | semidirect |
| 6. #22558098 | C2 | semidirect |
| 7. C67×#1997 | C2 | semidirect |
| 188. #1997 | D67 | semidirect |
| 192. C67 | #10110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571590 | 2 |
| #22571330 | 2 |
| #22570605 | 2 |
| #22558800 | 2 |
| #22558627 | 2 |
| #22558098 | 2 |
| C67×#1997 | 2 |
| #10110 | 67 |