Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
848 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 104 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×#10587547 | C2 | semidirect |
| 2. #11763777 | C2 | semidirect |
| 3. #11763751 | C2 | semidirect |
| 6. C22×D4×C17 | C4 | semidirect |
| 11. C2×D4×D17 | C4 | semidirect |
| 13. C22×D68 | C4 | semidirect |
| 16. C2×C4⋊#595 | C22 | semidirect |
| 17. C2×#63242 | C22 | semidirect |
| 87. D4×C17 | C22⋊C4 | semidirect |
| 98. D68 | C22⋊C4 | semidirect |
| 111. C22×C17 | #102 | semidirect |
| 124. C2×D17 | #102 | semidirect |
| 155. C22×D4 | #595 | semidirect |
| 164. C17 | #1786 | semidirect |
| 232. D4 | C22⋊#595 | semidirect |
| 269. C22 | #10587547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587547 | 2 |
| #11763777 | 2 |
| #11763751 | 2 |
| C22×D4×D17 | 2 |
| #1786 | 17 |