Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
498 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22561135 | C2 | semidirect |
| 3. #22558922 | C2 | semidirect |
| 4. #22558734 | C2 | semidirect |
| 5. #22558079 | C2 | semidirect |
| 6. #22558066 | C2 | semidirect |
| 7. C67×#2992 | C2 | semidirect |
| 9. #16863786 | C4 | semidirect |
| 10. #16863762 | C4 | semidirect |
| 217. #2992 | D67 | semidirect |
| 223. C67 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571224 | 2 |
| #22561135 | 2 |
| #22558922 | 2 |
| #22558734 | 2 |
| #22558079 | 2 |
| #22558066 | 2 |
| C67×#2992 | 2 |
| #9378 | 67 |