Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
374 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 103 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×C4×Dic34 | C2 | semidirect |
| 3. C2×#10587481 | C2 | semidirect |
| 5. #11762571 | C2 | semidirect |
| 6. #11762564 | C2 | semidirect |
| 16. C2×#63229 | C4 | semidirect |
| 82. C2×C4×C17 | SD16 | semidirect |
| 98. Dic34 | C22⋊C4 | semidirect |
| 158. C17 | #1880 | semidirect |
| 225. C2×C4 | #63229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63229 | 2 |
| C2×C4×Dic34 | 2 |
| C2×#10587481 | 2 |
| C2×#10587503 | 2 |
| #11762571 | 2 |
| #11762564 | 2 |
| C17×#390 | 2 |
| #1880 | 17 |