Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
372 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 372 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. #22558955 | C2 | semidirect |
| 3. C2×#16863148 | C2 | semidirect |
| 6. #22558060 | C2 | semidirect |
| 7. C67×#1283 | C2 | semidirect |
| 161. #1283 | D67 | semidirect |
| 162. C67 | #8606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568854 | 2 |
| #22558955 | 2 |
| C2×#16863148 | 2 |
| #22558597 | 2 |
| #22558594 | 2 |
| #22558060 | 2 |
| C67×#1283 | 2 |
| #8606 | 67 |