Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
428 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22560202 | C2 | semidirect |
| 3. #22558964 | C2 | semidirect |
| 6. C2×#16863126 | C2 | semidirect |
| 7. C67×#1292 | C2 | semidirect |
| 195. #1292 | D67 | semidirect |
| 196. C67 | #10459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569683 | 2 |
| #22560202 | 2 |
| #22558964 | 2 |
| #22558884 | 2 |
| #22558659 | 2 |
| C2×#16863126 | 2 |
| C67×#1292 | 2 |
| #10459 | 67 |