Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
240 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 21. #10587478 | C4 | semidirect |
| 73. #3622 | C4⋊C4 | semidirect |
| 120. C17 | #1943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587478 | 2 |
| C2×#10587479 | 2 |
| C2×#10587486 | 2 |
| #11762708 | 2 |
| #11762705 | 2 |
| #11762572 | 2 |
| C17×#340 | 2 |
| #1943 | 17 |