Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
488 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 205 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. #11762864 | C2 | direct (N × H) |
| 3. C2×#10587485 | C2 | semidirect |
| 5. C2×#10587474 | C2 | semidirect |
| 6. C2×C17×#97 | C2 | semidirect |
| 18. C17×#97 | C22 | semidirect |
| 20. #10587485 | C22 | semidirect |
| 21. #10587474 | C22 | semidirect |
| 91. C2×#97 | D17 | semidirect |
| 92. C2×C17 | #432 | semidirect |
| 111. #97 | C2×D17 | semidirect |
| 112. C17 | C2×#432 | semidirect |
| 177. C2 | #11762864 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D17 | 2 |
| #11762864 | 2 |
| C2×#10587485 | 2 |
| C2×#10587491 | 2 |
| C2×#10587474 | 2 |
| C2×C17×#97 | 2 |
| C2×#432 | 17 |