Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
392 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #11762869 | C2 | semidirect |
| 3. #11762833 | C2 | semidirect |
| 5. M16×Dic17 | C2 | semidirect |
| 6. C17×#423 | C2 | semidirect |
| 16. C17×C4⋊C8 | C22 | semidirect |
| 18. #10587486 | C22 | semidirect |
| 19. C8×Dic17 | C22 | semidirect |
| 20. C4⋊#3622 | C22 | semidirect |
| 75. #423 | D17 | semidirect |
| 92. C4⋊C8 | C2×D17 | semidirect |
| 96. C17 | #2921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587558 | 2 |
| #11762869 | 2 |
| #11762833 | 2 |
| #11762772 | 2 |
| M16×Dic17 | 2 |
| C17×#423 | 2 |
| #2921 | 17 |