Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11762793 | C2 | semidirect |
| 3. C2×#10587494 | C2 | semidirect |
| 4. #11762581 | C2 | semidirect |
| 5. C17×#568 | C2 | semidirect |
| 35. M16×C17 | D4 | semidirect |
| 81. #568 | D17 | semidirect |
| 105. C17 | #1914 | semidirect |
| 123. M16 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763373 | 2 |
| #11762793 | 2 |
| C2×#10587494 | 2 |
| #11762581 | 2 |
| C17×#568 | 2 |
| #1914 | 17 |