Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 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×#10587618 | C2 | semidirect |
| 2. C2×#10587587 | C2 | semidirect |
| 3. #11763076 | C2 | direct (N × H) |
| 4. C2×#10587490 | C2 | semidirect |
| 5. C2×#10587504 | C2 | semidirect |
| 6. C22×D8×C17 | C2 | semidirect |
| 12. C2×D8×C17 | C22 | semidirect |
| 16. #10587618 | C22 | semidirect |
| 21. #10587587 | C22 | semidirect |
| 24. #10587504 | C22 | semidirect |
| 25. #10587490 | C22 | semidirect |
| 104. C22×D8 | D17 | semidirect |
| 112. C2×C17 | #472 | semidirect |
| 124. C2×D8 | C2×D17 | semidirect |
| 134. C17 | C2×#472 | semidirect |
| 215. C2 | #11763076 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587618 | 2 |
| C2×#10587587 | 2 |
| #11763076 | 2 |
| C2×#10587490 | 2 |
| C2×#10587504 | 2 |
| C22×D8×C17 | 2 |
| C2×#472 | 17 |