Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
632 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 632 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. #22569276 | C2 | semidirect |
| 3. #22560175 | C2 | semidirect |
| 4. #22558337 | C2 | semidirect |
| 5. C67×#2126 | C2 | semidirect |
| 8. #16863578 | C4 | semidirect |
| 10. #16863568 | C4 | semidirect |
| 197. #2126 | D67 | semidirect |
| 200. C67 | #13054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569557 | 2 |
| #22569276 | 2 |
| #22560175 | 2 |
| #22558337 | 2 |
| C67×#2126 | 2 |
| #13054 | 67 |