Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
224 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 66 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×#10587529 | C2 | semidirect |
| 2. C2×#10587536 | C2 | semidirect |
| 3. #11763723 | C2 | direct (N × H) |
| 17. #10587536 | C22 | semidirect |
| 19. #10587529 | C22 | semidirect |
| 84. C2×C17 | #359 | semidirect |
| 103. C17 | C2×#359 | semidirect |
| 165. C2 | #11763723 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587529 | 2 |
| C2×#10587536 | 2 |
| #11763723 | 2 |
| C2×#10587598 | 2 |
| C2×#359 | 17 |