Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
312 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22562010 | C2 | semidirect |
| 3. C4⋊C16×D67 | C2 | semidirect |
| 4. #22558191 | C2 | semidirect |
| 5. #22558168 | C2 | semidirect |
| 6. #22558166 | C2 | semidirect |
| 7. C67×#1338 | C2 | semidirect |
| 154. #1338 | D67 | semidirect |
| 157. C67 | #11625 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569183 | 2 |
| #22562010 | 2 |
| C4⋊C16×D67 | 2 |
| #22558191 | 2 |
| #22558168 | 2 |
| #22558166 | 2 |
| C67×#1338 | 2 |
| #11625 | 67 |