Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
702 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 702 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. #11762737 | C2 | semidirect |
| 3. #11762724 | C2 | semidirect |
| 4. #11762688 | C2 | semidirect |
| 5. #11762682 | C2 | semidirect |
| 6. #11762665 | C2 | semidirect |
| 7. C22×C22⋊C4×C17 | C2 | semidirect |
| 19. C2×#63227 | C22 | semidirect |
| 20. C2×#63225 | C22 | semidirect |
| 21. #10587502 | C22 | semidirect |
| 22. #10587502 | C22 | semidirect |
| 93. C22×C22⋊C4 | D17 | semidirect |
| 120. C17 | #2622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587639 | 2 |
| #11762737 | 2 |
| #11762724 | 2 |
| #11762688 | 2 |
| #11762682 | 2 |
| #11762665 | 2 |
| C22×C22⋊C4×C17 | 2 |
| #2622 | 17 |