Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
508 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 165 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. #11762748 | C2 | semidirect |
| 3. #11762742 | C2 | semidirect |
| 4. #11762729 | C2 | semidirect |
| 34. C22×C4×C17 | Q8 | semidirect |
| 128. C17 | #2627 | semidirect |
| 140. C22×C4 | Dic34 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587610 | 2 |
| #11762748 | 2 |
| #11762742 | 2 |
| #11762729 | 2 |
| #11762682 | 2 |
| #11762672 | 2 |
| #11762669 | 2 |
| C22×C4⋊C4×C17 | 2 |
| #2627 | 17 |