Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 3. #11762907 | C2 | semidirect |
| 4. C4×#63230 | C2 | semidirect |
| 5. #11762845 | C2 | semidirect |
| 6. #11762818 | C2 | semidirect |
| 8. #11762765 | C2 | semidirect |
| 9. C17×#519 | C2 | semidirect |
| 13. C4×Q8×C17 | C22 | semidirect |
| 17. C2×#63230 | C4 | semidirect |
| 26. #10587506 | C22 | semidirect |
| 28. #10587479 | C22 | semidirect |
| 29. #10587478 | C22 | semidirect |
| 30. #10587474 | C22 | semidirect |
| 31. C4×#3622 | C22 | semidirect |
| 35. C2×Q8×C17 | C2×C4 | semidirect |
| 53. #63230 | C2×C4 | semidirect |
| 54. #63230 | C2×C4 | semidirect |
| 59. C2×#3622 | C2×C4 | semidirect |
| 101. #519 | D17 | semidirect |
| 121. C4×Q8 | C2×D17 | semidirect |
| 135. C17 | #2949 | semidirect |
| 139. C2×Q8 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63230 | 2 |
| #11763283 | 2 |
| #11762907 | 2 |
| C4×#63230 | 2 |
| #11762845 | 2 |
| #11762818 | 2 |
| #11762813 | 2 |
| #11762765 | 2 |
| C17×#519 | 2 |
| #2949 | 17 |