Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 1. D4×Dic34 | C2 | semidirect |
| 2. #11763161 | C2 | semidirect |
| 3. #11763150 | C2 | semidirect |
| 4. #11763101 | C2 | semidirect |
| 5. #11763053 | C2 | semidirect |
| 6. #11763014 | C2 | semidirect |
| 7. #11762947 | C2 | semidirect |
| 8. C4×#63229 | C2 | semidirect |
| 9. #11762887 | C2 | semidirect |
| 10. #11762817 | C2 | semidirect |
| 167. C17 | #3329 | 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 |
| #11763101 | 2 |
| #11763053 | 2 |
| #11763014 | 2 |
| #11762947 | 2 |
| C4×#63229 | 2 |
| #11762887 | 2 |
| #11762817 | 2 |
| C17×#555 | 2 |
| #3329 | 17 |