Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×Dic34 | C2 | semidirect |
| 2. C2×#10587637 | C2 | semidirect |
| 3. #11762964 | C2 | semidirect |
| 4. #11762947 | C2 | semidirect |
| 5. #11762817 | C2 | semidirect |
| 6. #11762773 | C2 | semidirect |
| 23. C2×#63231 | C22 | semidirect |
| 24. C2×#63229 | C22 | semidirect |
| 27. #10587481 | C22 | semidirect |
| 49. C2×Dic34 | D4 | semidirect |
| 96. C22×C17 | #137 | semidirect |
| 136. C17 | #3004 | semidirect |
| 204. C22 | #10587637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic34 | 2 |
| C2×#10587637 | 2 |
| #11762964 | 2 |
| #11762947 | 2 |
| #11762817 | 2 |
| #11762773 | 2 |
| C17×#525 | 2 |
| #3004 | 17 |