Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763414 | C2 | semidirect |
| 2. #11763199 | C2 | semidirect |
| 3. #11763185 | C2 | semidirect |
| 4. #11763173 | C2 | semidirect |
| 5. #11763163 | C2 | semidirect |
| 6. #11763021 | C2 | semidirect |
| 7. #11763001 | C2 | semidirect |
| 8. #11762954 | C2 | semidirect |
| 9. #11762943 | C2 | semidirect |
| 10. #11762870 | C2 | semidirect |
| 11. C17×#535 | C2 | semidirect |
| 21. C2×#63230 | C22 | semidirect |
| 24. C2×#63228 | C22 | semidirect |
| 28. #10587560 | C22 | semidirect |
| 29. C4×D68 | C22 | semidirect |
| 30. #10587556 | C22 | semidirect |
| 31. #10587506 | C22 | semidirect |
| 34. #10587503 | C22 | semidirect |
| 36. C4⋊#3622 | C22 | semidirect |
| 37. #10587474 | C22 | semidirect |
| 38. C4×#3622 | C22 | semidirect |
| 123. #535 | D17 | semidirect |
| 167. C17 | #3220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763414 | 2 |
| #11763199 | 2 |
| #11763185 | 2 |
| #11763173 | 2 |
| #11763163 | 2 |
| #11763021 | 2 |
| #11763001 | 2 |
| #11762954 | 2 |
| #11762943 | 2 |
| #11762870 | 2 |
| C17×#535 | 2 |
| #3220 | 17 |