Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
368 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 202 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. #11763868 | C2 | direct (N × H) |
| 2. C2×#10587530 | C2 | semidirect |
| 3. C2×#10587538 | C2 | semidirect |
| 4. C2×#10587529 | C2 | semidirect |
| 5. C22×#63216 | C2 | semidirect |
| 14. #10587538 | C22 | semidirect |
| 18. C2×#63216 | C22 | semidirect |
| 19. #10587530 | C22 | semidirect |
| 20. #10587529 | C22 | semidirect |
| 73. C2×C17 | #504 | semidirect |
| 90. C17 | C2×#504 | semidirect |
| 137. C2 | #11763868 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763868 | 2 |
| C2×#10587530 | 2 |
| C2×#10587538 | 2 |
| C2×#10587529 | 2 |
| C22×#63216 | 2 |
| C2×#10587593 | 2 |
| C2×#504 | 17 |