Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
416 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22561818 | C2 | semidirect |
| 3. #22560237 | C2 | semidirect |
| 4. #22558222 | C2 | semidirect |
| 5. #22558220 | C2 | semidirect |
| 6. #22558218 | C2 | semidirect |
| 7. C67×#1347 | C2 | semidirect |
| 8. C2×#14524062 | C4 | semidirect |
| 12. #16863638 | C4 | semidirect |
| 14. #16863629 | C4 | semidirect |
| 17. #16863433 | C4 | semidirect |
| 197. #1347 | D67 | semidirect |
| 198. C67 | #11890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569788 | 2 |
| #22561818 | 2 |
| #22560237 | 2 |
| #22558222 | 2 |
| #22558220 | 2 |
| #22558218 | 2 |
| C67×#1347 | 2 |
| #11890 | 67 |