Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
412 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 170 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. #11763834 | C2 | direct (N × H) |
| 2. C2×#10587544 | C2 | semidirect |
| 3. C2×C4⋊#3624 | C2 | semidirect |
| 6. C2×#10587542 | C2 | semidirect |
| 7. C2×C4×#3624 | C2 | semidirect |
| 22. #10587544 | C22 | semidirect |
| 25. #10587542 | C22 | semidirect |
| 26. C4⋊#3624 | C22 | semidirect |
| 27. C4×#3624 | C22 | semidirect |
| 106. C2×C17 | #433 | semidirect |
| 130. C17 | C2×#433 | semidirect |
| 201. C2 | #11763834 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763834 | 2 |
| C2×#10587544 | 2 |
| C2×C4⋊#3624 | 2 |
| C2×#10587543 | 2 |
| C2×#10587542 | 2 |
| C2×C4×#3624 | 2 |
| C2×#10587578 | 2 |
| C2×#433 | 17 |