Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
480 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 173 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×#10587555 | C2 | semidirect |
| 3. #11763100 | C2 | direct (N × H) |
| 4. C2×#10587488 | C2 | semidirect |
| 6. C2×C17×C4⋊C8 | C2 | semidirect |
| 19. #10587555 | C22 | semidirect |
| 20. C17×C4⋊C8 | C22 | semidirect |
| 22. #10587488 | C22 | semidirect |
| 31. C2×D68 | Q8 | semidirect |
| 66. D68 | C2×Q8 | semidirect |
| 90. C2×C4⋊C8 | D17 | semidirect |
| 92. C2×C17 | #476 | semidirect |
| 111. C4⋊C8 | C2×D17 | semidirect |
| 113. C17 | C2×#476 | semidirect |
| 177. C2 | #11763100 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587555 | 2 |
| C2×C4×D68 | 2 |
| #11763100 | 2 |
| C2×#10587488 | 2 |
| C2×#10587492 | 2 |
| C2×C17×C4⋊C8 | 2 |
| C2×#476 | 17 |