Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
310 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22559610 | C2 | semidirect |
| 4. #22558264 | C2 | semidirect |
| 5. #22558189 | C2 | semidirect |
| 7. C67×#2254 | C2 | semidirect |
| 126. #2254 | D67 | semidirect |
| 132. C67 | #12408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573061 | 2 |
| #22562353 | 2 |
| #22559610 | 2 |
| #22558264 | 2 |
| #22558189 | 2 |
| #22558171 | 2 |
| C67×#2254 | 2 |
| #12408 | 67 |