Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 121 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×#10587556 | C2 | semidirect |
| 2. #11763208 | C2 | semidirect |
| 3. #11763163 | C2 | semidirect |
| 4. #11763142 | C2 | semidirect |
| 5. #11763137 | C2 | semidirect |
| 8. #11763116 | C2 | semidirect |
| 9. #11763109 | C2 | semidirect |
| 10. #11762862 | C2 | semidirect |
| 168. C17 | #3232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587556 | 2 |
| #11763208 | 2 |
| #11763163 | 2 |
| #11763142 | 2 |
| #11763137 | 2 |
| #11763125 | 2 |
| #11763120 | 2 |
| #11763116 | 2 |
| #11763109 | 2 |
| #11762862 | 2 |
| C17×#529 | 2 |
| #3232 | 17 |