Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
576 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 149 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. #11762735 | C2 | semidirect |
| 4. #11762726 | C2 | semidirect |
| 5. #11762720 | C2 | semidirect |
| 6. #11762686 | C2 | semidirect |
| 7. C2×#10587502 | C2 | semidirect |
| 8. C2×C17×C22⋊Q8 | C2 | semidirect |
| 105. C2×C22⋊Q8 | D17 | semidirect |
| 138. C17 | #2639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587616 | 2 |
| #11762748 | 2 |
| #11762735 | 2 |
| #11762726 | 2 |
| #11762720 | 2 |
| #11762686 | 2 |
| C2×#10587502 | 2 |
| C2×C17×C22⋊Q8 | 2 |
| #2639 | 17 |