Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 3. #22562081 | C2 | semidirect |
| 4. #22558415 | C2 | semidirect |
| 5. #22558403 | C2 | semidirect |
| 7. C67×#1398 | C2 | semidirect |
| 12. Dic1072 | C4 | semidirect |
| 13. #16863235 | C4 | semidirect |
| 90. #1398 | D67 | semidirect |
| 91. C67 | #13657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562529 | 2 |
| #22562096 | 2 |
| #22562081 | 2 |
| #22558415 | 2 |
| #22558403 | 2 |
| #22558397 | 2 |
| C67×#1398 | 2 |
| #13657 | 67 |