Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
436 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11763354 | C2 | semidirect |
| 2. #11763088 | C2 | semidirect |
| 3. #11763087 | C2 | semidirect |
| 4. #11763045 | C2 | semidirect |
| 5. #11763043 | C2 | semidirect |
| 6. #11763003 | C2 | semidirect |
| 7. #11763002 | C2 | semidirect |
| 8. C2×#10587485 | C2 | semidirect |
| 9. C17×#466 | C2 | semidirect |
| 82. C2×Dic17 | D8 | semidirect |
| 115. #466 | D17 | semidirect |
| 150. C17 | #3245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763354 | 2 |
| #11763088 | 2 |
| #11763087 | 2 |
| #11763045 | 2 |
| #11763043 | 2 |
| #11763003 | 2 |
| #11763002 | 2 |
| C2×#10587485 | 2 |
| C17×#466 | 2 |
| #3245 | 17 |