Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
588 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22562670 | C2 | semidirect |
| 3. #22561036 | C2 | semidirect |
| 4. #22558703 | C2 | semidirect |
| 5. #22558633 | C2 | semidirect |
| 6. #22558041 | C2 | semidirect |
| 7. C67×#1303 | C2 | semidirect |
| 12. #16863677 | C4 | semidirect |
| 13. #16863592 | C4 | semidirect |
| 115. C4×Dic67 | D8 | semidirect |
| 222. #1303 | D67 | semidirect |
| 224. C67 | #9237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570210 | 2 |
| #22562670 | 2 |
| #22561036 | 2 |
| #22558703 | 2 |
| #22558633 | 2 |
| #22558041 | 2 |
| C67×#1303 | 2 |
| #9237 | 67 |