Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #11763437 | C2 | semidirect |
| 2. #11763173 | C2 | semidirect |
| 3. #11763168 | C2 | semidirect |
| 4. #11763163 | C2 | semidirect |
| 5. #11763155 | C2 | semidirect |
| 6. #11762814 | C2 | semidirect |
| 7. #11762810 | C2 | semidirect |
| 8. #11762805 | C2 | semidirect |
| 9. C2×#10587503 | C2 | semidirect |
| 10. #11762765 | C2 | semidirect |
| 27. #10587556 | C22 | semidirect |
| 28. #10587555 | C22 | semidirect |
| 29. #10587506 | C22 | semidirect |
| 30. #10587506 | C22 | semidirect |
| 31. #10587506 | C22 | semidirect |
| 36. #10587503 | C22 | semidirect |
| 37. #10587503 | C22 | semidirect |
| 38. #10587503 | C22 | semidirect |
| 39. #10587474 | C22 | semidirect |
| 40. C4×#3622 | C22 | semidirect |
| 176. C17 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763437 | 2 |
| #11763173 | 2 |
| #11763168 | 2 |
| #11763163 | 2 |
| #11763155 | 2 |
| #11762814 | 2 |
| #11762810 | 2 |
| #11762805 | 2 |
| C2×#10587503 | 2 |
| #11762765 | 2 |
| C17×#535 | 2 |
| #3136 | 17 |