Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 154 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 |
|---|---|---|
| 1. #11763856 | C2 | semidirect |
| 2. #11763850 | C2 | semidirect |
| 3. #11763734 | C2 | semidirect |
| 4. #11763727 | C2 | semidirect |
| 5. #11763725 | C2 | semidirect |
| 6. #11763700 | C2 | semidirect |
| 18. C17×D16 | C4 | semidirect |
| 19. #10587498 | C4 | semidirect |
| 20. #10587497 | C4 | semidirect |
| 21. #10587471 | C4 | semidirect |
| 34. D8×C17 | C2×C4 | semidirect |
| 37. Dic68 | C2×C4 | semidirect |
| 41. C16×C17 | C2×C4 | semidirect |
| 42. #63214 | C2×C4 | semidirect |
| 90. D16 | #595 | semidirect |
| 98. C17 | AGL(1,ℤ/16) | semidirect |
| 107. D8 | C2×#595 | semidirect |
| 118. C16 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763856 | 2 |
| #11763850 | 2 |
| #11763734 | 2 |
| #11763727 | 2 |
| #11763725 | 2 |
| #11763700 | 2 |
| #11763243 | 2 |
| AGL(1,ℤ/16) | 17 |