Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11763161 | C2 | semidirect |
| 3. #11763150 | C2 | semidirect |
| 4. #11763091 | C2 | semidirect |
| 5. #11763065 | C2 | semidirect |
| 6. #11763019 | C2 | semidirect |
| 7. #11762964 | C2 | semidirect |
| 8. C4×#63231 | C2 | semidirect |
| 10. #11762817 | C2 | semidirect |
| 162. C17 | #3328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic34 | 2 |
| #11763161 | 2 |
| #11763150 | 2 |
| #11763091 | 2 |
| #11763065 | 2 |
| #11763019 | 2 |
| #11762964 | 2 |
| C4×#63231 | 2 |
| #11762887 | 2 |
| #11762817 | 2 |
| C17×#556 | 2 |
| #3328 | 17 |