Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
416 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 3. #11763674 | C2 | semidirect |
| 7. C22×#3624 | C4 | semidirect |
| 14. C2×#63242 | C4 | semidirect |
| 16. C2×M16×C17 | C4 | semidirect |
| 17. C2×#63223 | C4 | semidirect |
| 20. C2×#63218 | C4 | semidirect |
| 112. C2×M16 | #595 | semidirect |
| 124. C17 | #1729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63242 | 2 |
| C2×#10587677 | 2 |
| #11763674 | 2 |
| C2×M16×D17 | 2 |
| #1729 | 17 |