Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
216 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 77 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. #11762858 | C2 | semidirect |
| 4. M16×Dic17 | C2 | semidirect |
| 5. #11762581 | C2 | semidirect |
| 6. #11762570 | C2 | semidirect |
| 15. C17×#101 | C4 | semidirect |
| 16. C17×#100 | C4 | semidirect |
| 114. #101 | Dic17 | semidirect |
| 115. #100 | Dic17 | semidirect |
| 118. C17 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762858 | 2 |
| #11762826 | 2 |
| C2×#10587508 | 2 |
| M16×Dic17 | 2 |
| #11762581 | 2 |
| #11762570 | 2 |
| C17×#413 | 2 |
| #1932 | 17 |