Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
560 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 233 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. #11762702 | C2 | semidirect |
| 3. #11762675 | C2 | semidirect |
| 4. #11762672 | C2 | semidirect |
| 5. C4⋊C4×Dic17 | C2 | semidirect |
| 6. C4×C4⋊Dic17 | C2 | semidirect |
| 7. C4×C22⋊Dic17 | C2 | semidirect |
| 11. C4×D4×C17 | C4 | semidirect |
| 108. C4×D4 | Dic17 | semidirect |
| 123. C17 | #2357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762712 | 2 |
| #11762702 | 2 |
| #11762675 | 2 |
| #11762672 | 2 |
| C4⋊C4×Dic17 | 2 |
| C4×C4⋊Dic17 | 2 |
| C4×C22⋊Dic17 | 2 |
| C2×C4×D4×C17 | 2 |
| #2357 | 17 |