Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
800 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 213 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×#10587555 | C2 | semidirect |
| 4. #11762730 | C2 | semidirect |
| 5. #11762715 | C2 | semidirect |
| 44. C22⋊C4×C17 | Q8 | semidirect |
| 62. C2×C4×C17 | C2×Q8 | semidirect |
| 78. C22×C17 | C4⋊Q8 | semidirect |
| 118. C17 | #2434 | semidirect |
| 142. C22⋊C4 | Dic34 | semidirect |
| 164. C2×C4 | C2×Dic34 | semidirect |
| 171. C22 | #10587555 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic34 | 2 |
| C2×#10587555 | 2 |
| C2×#10587610 | 2 |
| #11762730 | 2 |
| #11762715 | 2 |
| #11762684 | 2 |
| C4×C22⋊C4×C17 | 2 |
| #2434 | 17 |