Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
512 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 512 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. #22562683 | C2 | semidirect |
| 4. #22558639 | C2 | semidirect |
| 5. #22558112 | C2 | semidirect |
| 6. #22558041 | C2 | semidirect |
| 10. #16863678 | C4 | semidirect |
| 11. #16863593 | C4 | semidirect |
| 96. C4×Dic67 | SD16 | semidirect |
| 203. C67 | #9238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570236 | 2 |
| #22562683 | 2 |
| #22561038 | 2 |
| #22558639 | 2 |
| #22558112 | 2 |
| #22558041 | 2 |
| C67×#1502 | 2 |
| #9238 | 67 |