Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 101 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×#10587476 | C2 | semidirect |
| 4. C43×C17 | C2 | semidirect |
| 11. #10587561 | C4 | semidirect |
| 12. #10587560 | C4 | semidirect |
| 14. #10587555 | C4 | semidirect |
| 32. C42×C17 | D4 | semidirect |
| 64. C4×C17 | #104 | semidirect |
| 72. C43 | D17 | semidirect |
| 89. C17 | #1962 | semidirect |
| 109. C42 | D68 | semidirect |
| 137. C4 | #10587476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763359 | 2 |
| #11762833 | 2 |
| C2×#10587476 | 2 |
| C43×C17 | 2 |
| #1962 | 17 |