Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
848 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#16863194 | C2 | semidirect |
| 3. C2×#16863192 | C2 | semidirect |
| 4. #22560613 | C2 | semidirect |
| 5. #22560610 | C2 | semidirect |
| 6. #22560600 | C2 | semidirect |
| 7. C2×#355×C67 | C2 | semidirect |
| 11. #16864108 | C4 | semidirect |
| 254. C2×#355 | D67 | semidirect |
| 258. C67 | #12776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864108 | 2 |
| C2×#16863194 | 2 |
| C2×#16863192 | 2 |
| #22560613 | 2 |
| #22560610 | 2 |
| #22560600 | 2 |
| C2×#355×C67 | 2 |
| #12776 | 67 |