Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
272 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#10587665 | C2 | semidirect |
| 2. #11763906 | C2 | semidirect |
| 3. C22⋊#63241 | C2 | semidirect |
| 13. C2×#63241 | C22 | semidirect |
| 38. C22×D17 | C16 | semidirect |
| 61. C22×C17 | C2×C16 | semidirect |
| 68. C2×D17 | C2×C16 | semidirect |
| 84. D17 | C22⋊C16 | semidirect |
| 95. C17 | C2×C22⋊C16 | semidirect |
| 148. C22 | #10587665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587665 | 2 |
| #11763906 | 2 |
| C22⋊#63241 | 2 |
| C22×#63242 | 2 |
| C2×C22⋊C16 | 17 |