Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
788 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 202 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×#10587677 | C2 | semidirect |
| 2. #11763788 | C2 | direct (N × H) |
| 3. C2×#10587539 | C2 | semidirect |
| 4. C2×#10587551 | C2 | semidirect |
| 6. C23×C4×C17 | C4 | semidirect |
| 7. C22×C22⋊D17 | C4 | semidirect |
| 12. C2×#63252 | C4 | semidirect |
| 15. C22×C4×D17 | C4 | semidirect |
| 17. C22×Dic34 | C4 | semidirect |
| 20. #10587677 | C22 | semidirect |
| 23. #10587551 | C22 | semidirect |
| 24. #10587539 | C22 | semidirect |
| 34. C22×C4×C17 | C2×C4 | semidirect |
| 40. C2×C22⋊D17 | C2×C4 | semidirect |
| 56. C2×C4×D17 | C2×C4 | semidirect |
| 63. C2×Dic34 | C2×C4 | semidirect |
| 144. C2×C17 | #410 | semidirect |
| 160. C23×C4 | #595 | semidirect |
| 168. C17 | C2×#410 | semidirect |
| 207. C22×C4 | C2×#595 | semidirect |
| 285. C2 | #11763788 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587677 | 2 |
| #11763788 | 2 |
| C2×#10587539 | 2 |
| C2×#10587551 | 2 |
| C22×#63252 | 2 |
| C2×#410 | 17 |