Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 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×#10587610 | C2 | semidirect |
| 3. #11762736 | C2 | semidirect |
| 4. #11762722 | C2 | semidirect |
| 5. #11762700 | C2 | semidirect |
| 6. #11762670 | C2 | semidirect |
| 8. C4×C22⋊C4×C17 | C2 | semidirect |
| 12. C22×Dic34 | C22 | semidirect |
| 14. C2×C42×C17 | C22 | semidirect |
| 21. C2×C4⋊Dic17 | C22 | semidirect |
| 23. C2×#63225 | C22 | semidirect |
| 24. C17×#95 | C22 | semidirect |
| 25. #10587502 | C22 | semidirect |
| 26. #10587502 | C22 | semidirect |
| 112. C4×C22⋊C4 | D17 | semidirect |
| 133. C2×C42 | C2×D17 | semidirect |
| 136. #95 | C2×D17 | semidirect |
| 137. C17 | #2561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587610 | 2 |
| C22×#63227 | 2 |
| #11762736 | 2 |
| #11762722 | 2 |
| #11762700 | 2 |
| #11762670 | 2 |
| #11762664 | 2 |
| C4×C22⋊C4×C17 | 2 |
| #2561 | 17 |