Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×#10587536 | C2 | semidirect |
| 3. #11763816 | C2 | semidirect |
| 5. #11763679 | C2 | semidirect |
| 6. #11763674 | C2 | semidirect |
| 23. C17×#102 | C4 | semidirect |
| 24. #10587503 | C4 | semidirect |
| 25. #10587487 | C4 | semidirect |
| 26. #10587481 | C4 | semidirect |
| 135. #102 | #595 | semidirect |
| 136. C17 | #1866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587678 | 2 |
| C2×#10587536 | 2 |
| #11763816 | 2 |
| C2×#10587548 | 2 |
| #11763679 | 2 |
| #11763674 | 2 |
| #11762802 | 2 |
| #1866 | 17 |