Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
314 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 314 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. #22561963 | C2 | semidirect |
| 3. #22558963 | C2 | semidirect |
| 4. #22558261 | C2 | semidirect |
| 5. #22558253 | C2 | semidirect |
| 6. #22558251 | C2 | semidirect |
| 7. C67×#1363 | C2 | semidirect |
| 155. #1363 | D67 | semidirect |
| 158. C67 | #11980 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570781 | 2 |
| #22561963 | 2 |
| #22558963 | 2 |
| #22558261 | 2 |
| #22558253 | 2 |
| #22558251 | 2 |
| C67×#1363 | 2 |
| #11980 | 67 |