Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22561982 | C2 | semidirect |
| 3. #22561958 | C2 | semidirect |
| 4. #22561819 | C2 | semidirect |
| 5. #22560244 | C2 | semidirect |
| 6. #22558323 | C2 | semidirect |
| 7. C67×#2143 | C2 | semidirect |
| 64. C2×C16×C67 | D4 | semidirect |
| 185. #2143 | D67 | semidirect |
| 189. C67 | #13395 | semidirect |
| 239. C2×C16 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569786 | 2 |
| #22561982 | 2 |
| #22561958 | 2 |
| #22561819 | 2 |
| #22560244 | 2 |
| #22558323 | 2 |
| C67×#2143 | 2 |
| #13395 | 67 |