Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
680 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 163 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. C22×Dic536 | C2 | semidirect |
| 4. #22569076 | C2 | semidirect |
| 5. #22562270 | C2 | semidirect |
| 6. #22562258 | C2 | semidirect |
| 7. #22561967 | C2 | semidirect |
| 8. #22561928 | C2 | semidirect |
| 181. C67 | #33588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863836 | 2 |
| C22×Dic536 | 2 |
| #22570704 | 2 |
| #22569076 | 2 |
| #22562270 | 2 |
| #22562258 | 2 |
| #22561967 | 2 |
| #22561928 | 2 |
| C67×#2138 | 2 |
| #33588 | 67 |