Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
566 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 1. #22571401 | C2 | semidirect |
| 3. #22565375 | C2 | semidirect |
| 4. #22561128 | C2 | semidirect |
| 5. #22558810 | C2 | semidirect |
| 6. #22558066 | C2 | semidirect |
| 7. C67×#1490 | C2 | semidirect |
| 222. #1490 | D67 | semidirect |
| 224. C67 | #10005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571401 | 2 |
| #22570300 | 2 |
| #22565375 | 2 |
| #22561128 | 2 |
| #22558810 | 2 |
| #22558066 | 2 |
| C67×#1490 | 2 |
| #10005 | 67 |