Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 93 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. #11762833 | C2 | semidirect |
| 3. C2×#10587495 | C2 | semidirect |
| 5. C4×M16×C17 | C2 | semidirect |
| 81. C4×M16 | D17 | semidirect |
| 100. C17 | #1967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587561 | 2 |
| #11762833 | 2 |
| C2×#10587495 | 2 |
| C2×#10587494 | 2 |
| C4×M16×C17 | 2 |
| #1967 | 17 |