Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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. #11763286 | C2 | semidirect |
| 3. #11762909 | C2 | semidirect |
| 4. C4×#63229 | C2 | semidirect |
| 5. #11762845 | C2 | semidirect |
| 6. #11762817 | C2 | semidirect |
| 8. #11762765 | C2 | semidirect |
| 17. C2×#63229 | C4 | semidirect |
| 25. C4×Dic34 | C22 | semidirect |
| 27. #10587481 | C22 | semidirect |
| 28. #10587479 | C22 | semidirect |
| 29. #10587478 | C22 | semidirect |
| 30. #10587474 | C22 | semidirect |
| 31. C4×#3622 | C22 | semidirect |
| 42. C2×Dic34 | C2×C4 | semidirect |
| 52. #63229 | C2×C4 | semidirect |
| 53. #63229 | C2×C4 | semidirect |
| 59. C2×#3622 | C2×C4 | semidirect |
| 135. C17 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63229 | 2 |
| #11763286 | 2 |
| #11762909 | 2 |
| C4×#63229 | 2 |
| #11762845 | 2 |
| #11762817 | 2 |
| #11762814 | 2 |
| #11762765 | 2 |
| C17×#518 | 2 |
| #2949 | 17 |