Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
520 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 520 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×#10587636 | C2 | semidirect |
| 2. C23×#3622 | C2 | semidirect |
| 3. #11763320 | C2 | semidirect |
| 4. #11763048 | C2 | semidirect |
| 5. #11763043 | C2 | semidirect |
| 6. #11763040 | C2 | semidirect |
| 7. #11763036 | C2 | semidirect |
| 8. #11762845 | C2 | semidirect |
| 9. #11762805 | C2 | semidirect |
| 10. #11762803 | C2 | semidirect |
| 11. C17×#525 | C2 | semidirect |
| 23. C2×#63231 | C22 | semidirect |
| 24. C2×#63230 | C22 | semidirect |
| 25. C2×#63229 | C22 | semidirect |
| 26. C2×#63228 | C22 | semidirect |
| 37. #10587506 | C22 | semidirect |
| 38. #10587503 | C22 | semidirect |
| 39. #10587481 | C22 | semidirect |
| 40. #10587480 | C22 | semidirect |
| 41. #10587479 | C22 | semidirect |
| 42. #10587478 | C22 | semidirect |
| 83. C2×#3622 | D4 | semidirect |
| 131. C22×C17 | #135 | semidirect |
| 146. #525 | D17 | semidirect |
| 191. C17 | #3050 | semidirect |
| 281. C22 | #10587636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587636 | 2 |
| C23×#3622 | 2 |
| #11763320 | 2 |
| #11763048 | 2 |
| #11763043 | 2 |
| #11763040 | 2 |
| #11763036 | 2 |
| #11762845 | 2 |
| #11762805 | 2 |
| #11762803 | 2 |
| C17×#525 | 2 |
| #3050 | 17 |