Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
388 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #22560960 | C2 | semidirect |
| 5. #22558323 | C2 | semidirect |
| 6. #22558292 | C2 | semidirect |
| 7. C67×#2161 | C2 | semidirect |
| 17. #16863207 | C4 | semidirect |
| 145. #2161 | D67 | semidirect |
| 151. C67 | #12944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863517 | 2 |
| #22561946 | 2 |
| #22561936 | 2 |
| #22560960 | 2 |
| #22558323 | 2 |
| #22558292 | 2 |
| C67×#2161 | 2 |
| #12944 | 67 |