Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 2. #11763122 | C2 | direct (N × H) |
| 3. C2×#10587478 | C2 | semidirect |
| 4. C2×#10587480 | C2 | semidirect |
| 5. C2×C22⋊#3622 | C2 | semidirect |
| 6. C22×C4⋊C4×C17 | C2 | semidirect |
| 14. C2×C4⋊C4×C17 | C22 | semidirect |
| 20. C22⋊#3622 | C22 | semidirect |
| 21. #10587480 | C22 | semidirect |
| 22. #10587478 | C22 | semidirect |
| 91. C22×C4⋊C4 | D17 | semidirect |
| 97. C2×C17 | #480 | semidirect |
| 113. C2×C4⋊C4 | C2×D17 | semidirect |
| 118. C17 | C2×#480 | semidirect |
| 187. C2 | #11763122 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587616 | 2 |
| #11763122 | 2 |
| C2×#10587478 | 2 |
| C2×#10587480 | 2 |
| C2×C22⋊#3622 | 2 |
| C22×C4⋊C4×C17 | 2 |
| C2×#480 | 17 |