Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#10587587 | C2 | semidirect |
| 3. C2×#10587508 | C2 | semidirect |
| 4. C2×#10587496 | C2 | semidirect |
| 5. #11762573 | C2 | semidirect |
| 6. #11762563 | C2 | semidirect |
| 7. C17×#408 | C2 | semidirect |
| 14. C2×#63231 | C4 | semidirect |
| 15. C2×#63230 | C4 | semidirect |
| 16. C2×#63229 | C4 | semidirect |
| 17. C2×#63228 | C4 | semidirect |
| 128. #408 | D17 | semidirect |
| 159. C17 | #1876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587636 | 2 |
| C2×#10587587 | 2 |
| C2×#10587508 | 2 |
| C2×#10587496 | 2 |
| #11762573 | 2 |
| #11762563 | 2 |
| C17×#408 | 2 |
| #1876 | 17 |