Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
528 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22561133 | C2 | semidirect |
| 5. #22558708 | C2 | semidirect |
| 6. #22558060 | C2 | semidirect |
| 7. C67×#3165 | C2 | semidirect |
| 108. M16×C67 | SD16 | semidirect |
| 193. #3165 | D67 | semidirect |
| 198. C67 | #10201 | semidirect |
| 289. M16 | #11761615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571521 | 2 |
| #22571337 | 2 |
| #22561133 | 2 |
| #22561128 | 2 |
| #22558708 | 2 |
| #22558060 | 2 |
| C67×#3165 | 2 |
| #10201 | 67 |