Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10587637 | C2 | semidirect |
| 2. C2×#10587618 | C2 | semidirect |
| 3. C2×#10587636 | C2 | semidirect |
| 4. C22×#63229 | C2 | semidirect |
| 5. #11763385 | C2 | semidirect |
| 6. #11763204 | C2 | semidirect |
| 7. #11763196 | C2 | semidirect |
| 8. #11763191 | C2 | semidirect |
| 9. #11763181 | C2 | semidirect |
| 10. #11762765 | C2 | semidirect |
| 11. C17×#535 | C2 | semidirect |
| 23. C2×#63231 | C22 | semidirect |
| 24. C2×#63231 | C22 | semidirect |
| 25. C2×#63230 | C22 | semidirect |
| 30. C2×#63229 | C22 | semidirect |
| 31. C2×#63229 | C22 | semidirect |
| 34. C2×#63228 | C22 | semidirect |
| 39. #10587561 | C22 | semidirect |
| 40. #10587555 | C22 | semidirect |
| 41. #10587474 | C22 | semidirect |
| 42. C4×#3622 | C22 | semidirect |
| 83. #63223 | D4 | semidirect |
| 84. C2×#3622 | D4 | semidirect |
| 148. #535 | D17 | semidirect |
| 191. C17 | #3154 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587637 | 2 |
| C2×#10587618 | 2 |
| C2×#10587636 | 2 |
| C22×#63229 | 2 |
| #11763385 | 2 |
| #11763204 | 2 |
| #11763196 | 2 |
| #11763191 | 2 |
| #11763181 | 2 |
| #11762765 | 2 |
| C17×#535 | 2 |
| #3154 | 17 |