Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
534 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. #22565592 | C2 | semidirect |
| 5. #22558812 | C2 | semidirect |
| 6. #22558655 | C2 | semidirect |
| 7. C67×#1285 | C2 | semidirect |
| 208. #1285 | D67 | semidirect |
| 209. C67 | #10007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571401 | 2 |
| #22570332 | 2 |
| #22565592 | 2 |
| #22561127 | 2 |
| #22558812 | 2 |
| #22558655 | 2 |
| C67×#1285 | 2 |
| #10007 | 67 |