Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
316 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22562406 | C2 | semidirect |
| 4. #22558220 | C2 | semidirect |
| 6. #22558149 | C2 | semidirect |
| 7. C67×#2086 | C2 | semidirect |
| 156. #2086 | D67 | semidirect |
| 160. C67 | #12290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571561 | 2 |
| #22562406 | 2 |
| #22562389 | 2 |
| #22558220 | 2 |
| #22558217 | 2 |
| #22558149 | 2 |
| C67×#2086 | 2 |
| #12290 | 67 |