Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11763146 | C2 | semidirect |
| 3. #11763101 | C2 | semidirect |
| 4. #11763051 | C2 | semidirect |
| 5. C4×Dic68 | C2 | semidirect |
| 7. #107×D17 | C2 | semidirect |
| 8. C17×#500 | C2 | semidirect |
| 58. D68 | Q16 | semidirect |
| 81. #500 | D17 | semidirect |
| 111. C17 | #3338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763520 | 2 |
| #11763146 | 2 |
| #11763101 | 2 |
| #11763051 | 2 |
| C4×Dic68 | 2 |
| C8×D68 | 2 |
| #107×D17 | 2 |
| C17×#500 | 2 |
| #3338 | 17 |