Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
226 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 57 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. C22×Dic68 | C2 | semidirect |
| 2. C2×#10587471 | C2 | semidirect |
| 4. #11762614 | C2 | semidirect |
| 5. C17×C22⋊C16 | C2 | semidirect |
| 32. Dic68 | D4 | semidirect |
| 55. C22×C17 | SD32 | semidirect |
| 69. C22⋊C16 | D17 | semidirect |
| 86. C17 | #2185 | semidirect |
| 127. C22 | #10587471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic68 | 2 |
| C2×#10587471 | 2 |
| #11763045 | 2 |
| #11762614 | 2 |
| C17×C22⋊C16 | 2 |
| #2185 | 17 |