Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#10587636 | C2 | semidirect |
| 2. #11763480 | C2 | semidirect |
| 3. #11763183 | C2 | semidirect |
| 4. #11763040 | C2 | semidirect |
| 5. #11763016 | C2 | semidirect |
| 6. #11763004 | C2 | semidirect |
| 7. #11762969 | C2 | semidirect |
| 8. #11762954 | C2 | semidirect |
| 9. C4×#63229 | C2 | semidirect |
| 10. D4×#3622 | C2 | semidirect |
| 11. C17×#547 | C2 | semidirect |
| 72. #63229 | D4 | semidirect |
| 130. C4×C17 | #135 | semidirect |
| 137. #547 | D17 | semidirect |
| 182. C17 | #3284 | semidirect |
| 272. C4 | #10587636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587636 | 2 |
| #11763480 | 2 |
| #11763183 | 2 |
| #11763040 | 2 |
| #11763016 | 2 |
| #11763004 | 2 |
| #11762969 | 2 |
| #11762954 | 2 |
| C4×#63229 | 2 |
| D4×#3622 | 2 |
| C17×#547 | 2 |
| #3284 | 17 |