Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
432 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×C22⋊#3622 | C2 | semidirect |
| 3. C2×#10587491 | C2 | semidirect |
| 4. #11762563 | C2 | semidirect |
| 5. C23×C8×C17 | C2 | semidirect |
| 31. C2×C22⋊D17 | C8 | semidirect |
| 42. C2×C8×C17 | D4 | semidirect |
| 61. C22×D17 | C2×C8 | semidirect |
| 78. C2×Dic17 | C2×C8 | semidirect |
| 89. C22×C17 | C22⋊C8 | semidirect |
| 107. C23×C8 | D17 | semidirect |
| 134. C17 | #1869 | semidirect |
| 159. C2×C8 | C22⋊D17 | semidirect |
| 207. C22 | #10587491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D17 | 2 |
| C2×C22⋊#3622 | 2 |
| C2×#10587491 | 2 |
| #11762563 | 2 |
| C23×C8×C17 | 2 |
| #1869 | 17 |