Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10587595 | C2 | semidirect |
| 3. #11763380 | C2 | semidirect |
| 4. #11763290 | C2 | semidirect |
| 5. #11763030 | C2 | semidirect |
| 6. #11763023 | C2 | semidirect |
| 7. #11763018 | C2 | semidirect |
| 8. #11763013 | C2 | semidirect |
| 9. #11762837 | C2 | semidirect |
| 10. C2×#10587481 | C2 | semidirect |
| 11. C17×#417 | C2 | semidirect |
| 150. #417 | D17 | semidirect |
| 189. C17 | #3046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587595 | 2 |
| C2×#10587636 | 2 |
| #11763380 | 2 |
| #11763290 | 2 |
| #11763030 | 2 |
| #11763023 | 2 |
| #11763018 | 2 |
| #11763013 | 2 |
| #11762837 | 2 |
| C2×#10587481 | 2 |
| C17×#417 | 2 |
| #3046 | 17 |