Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
290 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. C4⋊C4×Dic17 | C2 | semidirect |
| 5. #11762571 | C2 | semidirect |
| 6. #11762563 | C2 | semidirect |
| 7. C2×C17×#107 | C2 | semidirect |
| 20. #10587492 | C4 | semidirect |
| 111. C2×#107 | D17 | semidirect |
| 140. C17 | #1925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587492 | 2 |
| C2×#10587480 | 2 |
| #11762710 | 2 |
| C4⋊C4×Dic17 | 2 |
| #11762571 | 2 |
| #11762563 | 2 |
| C2×C17×#107 | 2 |
| #1925 | 17 |