Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
512 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 210 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. #11763816 | C2 | semidirect |
| 4. #11763815 | C2 | semidirect |
| 5. #11763810 | C2 | semidirect |
| 24. #10587544 | C22 | semidirect |
| 25. C4⋊#3624 | C22 | semidirect |
| 102. D17 | #424 | semidirect |
| 122. C17 | C2×#424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D17⋊M16 | 2 |
| C22×#63242 | 2 |
| #11763816 | 2 |
| #11763815 | 2 |
| #11763810 | 2 |
| #117×D17 | 2 |
| C2×#424 | 17 |