Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 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. #11763421 | C2 | direct (N × H) |
| 2. C2×#10587555 | C2 | semidirect |
| 4. C2×#10587556 | C2 | semidirect |
| 5. C2×#10587575 | C2 | semidirect |
| 7. C2×C4×Dic34 | C2 | semidirect |
| 24. #10587575 | C22 | semidirect |
| 26. #10587556 | C22 | semidirect |
| 27. #10587555 | C22 | semidirect |
| 28. C4×Dic34 | C22 | semidirect |
| 91. C2×C17 | #541 | semidirect |
| 114. C17 | C2×#541 | semidirect |
| 168. C2 | #11763421 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763421 | 2 |
| C2×#10587555 | 2 |
| C2×#10587565 | 2 |
| C2×#10587556 | 2 |
| C2×#10587575 | 2 |
| C2×#10587610 | 2 |
| C2×C4×Dic34 | 2 |
| C2×C17×#117 | 2 |
| C2×#541 | 17 |