Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 398 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. #11763519 | C2 | semidirect |
| 3. #11763156 | C2 | semidirect |
| 4. #11763124 | C2 | semidirect |
| 5. #11763104 | C2 | semidirect |
| 6. #11763058 | C2 | semidirect |
| 7. #11763009 | C2 | semidirect |
| 8. #11762970 | C2 | semidirect |
| 9. #11762888 | C2 | semidirect |
| 10. #11762809 | C2 | semidirect |
| 11. C4×Q16×C17 | C2 | semidirect |
| 132. C4×Q16 | D17 | semidirect |
| 169. C17 | #3333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763519 | 2 |
| #11763481 | 2 |
| #11763156 | 2 |
| #11763124 | 2 |
| #11763104 | 2 |
| #11763058 | 2 |
| #11763009 | 2 |
| #11762970 | 2 |
| #11762888 | 2 |
| #11762809 | 2 |
| C4×Q16×C17 | 2 |
| #3333 | 17 |