Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
550 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22571339 | C2 | semidirect |
| 3. #22570603 | C2 | semidirect |
| 4. #22561131 | C2 | semidirect |
| 5. #22561128 | C2 | semidirect |
| 6. #22558705 | C2 | semidirect |
| 7. C67×#1283 | C2 | semidirect |
| 207. #1283 | D67 | semidirect |
| 208. C67 | #10200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571519 | 2 |
| #22571339 | 2 |
| #22570603 | 2 |
| #22561131 | 2 |
| #22561128 | 2 |
| #22558705 | 2 |
| C67×#1283 | 2 |
| #10200 | 67 |