Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
264 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 66 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. #11763827 | C2 | semidirect |
| 2. #11763753 | C2 | semidirect |
| 3. #11763660 | C2 | semidirect |
| 7. C17×#127 | C4 | semidirect |
| 12. D4×Dic17 | C4 | semidirect |
| 14. #10587555 | C4 | semidirect |
| 95. #127 | #595 | semidirect |
| 108. C17 | #1517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763827 | 2 |
| #11763753 | 2 |
| #11763660 | 2 |
| #11763357 | 2 |
| #1517 | 17 |