Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10587587 | C2 | semidirect |
| 2. #11763387 | C2 | semidirect |
| 3. #11763052 | C2 | semidirect |
| 4. #11763047 | C2 | semidirect |
| 5. #11763042 | C2 | semidirect |
| 6. C2×#10587489 | C2 | semidirect |
| 7. #11762810 | C2 | semidirect |
| 8. C2×C17×#135 | C2 | semidirect |
| 48. C2×C8×C17 | D4 | semidirect |
| 103. C2×#135 | D17 | semidirect |
| 138. C17 | #3061 | semidirect |
| 161. C2×C8 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587587 | 2 |
| #11763387 | 2 |
| #11763052 | 2 |
| #11763047 | 2 |
| #11763042 | 2 |
| C2×#10587489 | 2 |
| #11762810 | 2 |
| C2×C17×#135 | 2 |
| #3061 | 17 |