Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
142 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 44 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 |
|---|---|---|
| 2. #11763849 | C2 | semidirect |
| 3. #11763734 | C2 | semidirect |
| 4. #11763728 | C2 | semidirect |
| 6. #11763700 | C2 | semidirect |
| 18. C17×Q32 | C4 | semidirect |
| 19. #10587500 | C4 | semidirect |
| 20. #10587499 | C4 | semidirect |
| 21. #10587471 | C4 | semidirect |
| 83. Q32 | #595 | semidirect |
| 93. C17 | #2180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763855 | 2 |
| #11763849 | 2 |
| #11763734 | 2 |
| #11763728 | 2 |
| #11763726 | 2 |
| #11763700 | 2 |
| #11763251 | 2 |
| #2180 | 17 |