Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
348 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 82 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×#10587533 | C2 | semidirect |
| 2. C2×#10587549 | C2 | semidirect |
| 4. C2×C8×#595 | C2 | semidirect |
| 5. (C2×#595)⋊Q8 | C2 | semidirect |
| 15. C2×SD16×C17 | C4 | semidirect |
| 16. C2×#63230 | C4 | semidirect |
| 17. C2×#63229 | C4 | semidirect |
| 20. C2×#63219 | C4 | semidirect |
| 78. C2×#595 | SD16 | semidirect |
| 102. C8×C17 | C22⋊C4 | semidirect |
| 103. #3622 | C22⋊C4 | semidirect |
| 147. C2×SD16 | #595 | semidirect |
| 159. C17 | #1968 | semidirect |
| 236. C8 | C22⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587533 | 2 |
| C2×#10587549 | 2 |
| C2×#10587547 | 2 |
| C2×C8×#595 | 2 |
| (C2×#595)⋊Q8 | 2 |
| #11763761 | 2 |
| C2×SD16×D17 | 2 |
| #1968 | 17 |