Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
852 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 138 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×#10587543 | C2 | semidirect |
| 2. C2×C22⋊#3624 | C2 | semidirect |
| 11. C22×#3624 | C22 | semidirect |
| 19. C23×D17 | C8 | semidirect |
| 72. C22×C17 | C22⋊C8 | semidirect |
| 85. C2×D17 | C22⋊C8 | semidirect |
| 109. C17 | #1779 | semidirect |
| 175. C22 | #10587543 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587543 | 2 |
| C2×C22⋊#3624 | 2 |
| C23×C4×D17 | 2 |
| #1779 | 17 |