Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
512 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 218 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. #11763816 | C2 | direct (N × H) |
| 4. C2×#10587544 | C2 | semidirect |
| 5. C2×C4⋊#3624 | C2 | semidirect |
| 21. #10587544 | C22 | semidirect |
| 22. C4⋊#3624 | C22 | semidirect |
| 87. C2×C17 | #424 | semidirect |
| 108. C17 | C2×#424 | semidirect |
| 167. C2 | #11763816 | 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 |
| C22×#63242 | 2 |
| #11763816 | 2 |
| C2×#10587544 | 2 |
| C2×C4⋊#3624 | 2 |
| C2×#10587578 | 2 |
| C2×#424 | 17 |