Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
400 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10587485 | C2 | semidirect |
| 4. #11762563 | C2 | semidirect |
| 31. C22×Dic17 | C8 | semidirect |
| 86. C22×C17 | C4⋊C8 | semidirect |
| 100. Dic17 | C22⋊C8 | semidirect |
| 127. C17 | #1797 | semidirect |
| 194. C22 | #10587485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic17 | 2 |
| C2×#10587485 | 2 |
| C2×C22⋊#3622 | 2 |
| #11762563 | 2 |
| C2×C17×C22⋊C8 | 2 |
| #1797 | 17 |