Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
484 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 123 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×#10587605 | C2 | semidirect |
| 2. C2×#10587590 | C2 | semidirect |
| 3. #11763461 | C2 | semidirect |
| 4. #11763187 | C2 | semidirect |
| 5. #11763051 | C2 | semidirect |
| 6. #11763013 | C2 | semidirect |
| 7. #11762974 | C2 | semidirect |
| 8. #11762969 | C2 | semidirect |
| 9. #11762891 | C2 | semidirect |
| 10. C8×C22⋊D17 | C2 | semidirect |
| 11. C17×#467 | C2 | semidirect |
| 77. D136 | D4 | semidirect |
| 130. Dic17 | #135 | semidirect |
| 136. #467 | D17 | semidirect |
| 177. C17 | #3283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587605 | 2 |
| C2×#10587590 | 2 |
| #11763461 | 2 |
| #11763187 | 2 |
| #11763051 | 2 |
| #11763013 | 2 |
| #11762974 | 2 |
| #11762969 | 2 |
| #11762891 | 2 |
| C8×C22⋊D17 | 2 |
| C17×#467 | 2 |
| #3283 | 17 |