Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
820 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 820 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 |
|---|---|---|
| 1. C2×#10587504 | C2 | semidirect |
| 2. #11762773 | C2 | semidirect |
| 10. C2×#63223 | C22 | semidirect |
| 60. C22×C17 | #100 | semidirect |
| 82. C17 | #1783 | semidirect |
| 129. C22 | #10587504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587504 | 2 |
| #11762773 | 2 |
| C23×D4×C17 | 2 |
| #1783 | 17 |