Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
228 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#10587490 | C2 | semidirect |
| 2. #11762849 | C2 | semidirect |
| 3. #11762835 | C2 | semidirect |
| 6. #11762578 | C2 | semidirect |
| 120. C17 | #2063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587490 | 2 |
| #11762849 | 2 |
| #11762835 | 2 |
| #11762814 | 2 |
| C2×#10587504 | 2 |
| #11762578 | 2 |
| C2×C17×#102 | 2 |
| #2063 | 17 |