Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
460 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 202 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 |
|---|---|---|
| 3. #11763824 | C2 | direct (N × H) |
| 4. C2×#10587536 | C2 | semidirect |
| 5. C2×#10587535 | C2 | semidirect |
| 25. #10587536 | C22 | semidirect |
| 26. #10587535 | C22 | semidirect |
| 111. C2×C17 | #430 | semidirect |
| 136. C17 | C2×#430 | semidirect |
| 217. C2 | #11763824 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63243 | 2 |
| C2×D17⋊M16 | 2 |
| #11763824 | 2 |
| C2×#10587536 | 2 |
| C2×#10587535 | 2 |
| C2×M16×D17 | 2 |
| C2×#430 | 17 |