Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763544 | C2 | semidirect |
| 2. D4×Dic34 | C2 | semidirect |
| 3. #11763170 | C2 | semidirect |
| 4. #11763156 | C2 | semidirect |
| 5. #11763098 | C2 | semidirect |
| 6. #11763094 | C2 | semidirect |
| 7. #11763026 | C2 | semidirect |
| 9. #11762939 | C2 | semidirect |
| 10. #11762918 | C2 | semidirect |
| 11. C4×SD16×C17 | C2 | semidirect |
| 130. C4×SD16 | D17 | semidirect |
| 165. C17 | #3373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763544 | 2 |
| D4×Dic34 | 2 |
| #11763170 | 2 |
| #11763156 | 2 |
| #11763098 | 2 |
| #11763094 | 2 |
| #11763026 | 2 |
| #11763004 | 2 |
| #11762939 | 2 |
| #11762918 | 2 |
| C4×SD16×C17 | 2 |
| #3373 | 17 |