Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
178 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 59 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. #22561993 | C2 | semidirect |
| 3. #22558411 | C2 | semidirect |
| 4. #22558409 | C2 | semidirect |
| 5. #22558388 | C2 | semidirect |
| 6. #22558388 | C2 | semidirect |
| 7. C67×C22⋊C32 | C2 | semidirect |
| 94. C22⋊C32 | D67 | semidirect |
| 95. C67 | #13713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562295 | 2 |
| #22561993 | 2 |
| #22558411 | 2 |
| #22558409 | 2 |
| #22558388 | 2 |
| C67×C22⋊C32 | 2 |
| #13713 | 67 |