Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4×Dic34 | C2 | semidirect |
| 2. #11763142 | C2 | semidirect |
| 4. #11763113 | C2 | semidirect |
| 5. #11763028 | C2 | semidirect |
| 6. #11762964 | C2 | semidirect |
| 8. #11762914 | C2 | semidirect |
| 9. #11762909 | C2 | semidirect |
| 10. #11762866 | C2 | semidirect |
| 174. C17 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic34 | 2 |
| #11763142 | 2 |
| #11763125 | 2 |
| #11763113 | 2 |
| #11763028 | 2 |
| #11762964 | 2 |
| #11762947 | 2 |
| #11762914 | 2 |
| #11762909 | 2 |
| #11762866 | 2 |
| C17×#529 | 2 |
| #3117 | 17 |