Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
394 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22561053 | C2 | semidirect |
| 3. #22558997 | C2 | semidirect |
| 5. #22558891 | C2 | semidirect |
| 7. C67×#1299 | C2 | semidirect |
| 165. #1299 | D67 | semidirect |
| 166. C67 | #10489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571136 | 2 |
| #22561053 | 2 |
| #22558997 | 2 |
| #22558942 | 2 |
| #22558891 | 2 |
| #22558627 | 2 |
| C67×#1299 | 2 |
| #10489 | 67 |