Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
274 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22562348 | C2 | semidirect |
| 4. #22558261 | C2 | semidirect |
| 5. #22558180 | C2 | semidirect |
| 7. C67×#2255 | C2 | semidirect |
| 136. #2255 | D67 | semidirect |
| 142. C67 | #12401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22572782 | 2 |
| #22562348 | 2 |
| #22559729 | 2 |
| #22558261 | 2 |
| #22558180 | 2 |
| #22558168 | 2 |
| C67×#2255 | 2 |
| #12401 | 67 |