Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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. C2×#10587634 | C2 | semidirect |
| 3. #11762813 | C2 | semidirect |
| 4. #11762808 | C2 | semidirect |
| 5. #11762803 | C2 | semidirect |
| 6. C2×#10587480 | C2 | semidirect |
| 7. C17×#520 | C2 | semidirect |
| 10. #10587696 | C4 | semidirect |
| 17. C17×#117 | C22 | semidirect |
| 18. C2×C4⋊C4×C17 | C22 | semidirect |
| 20. C2×#63223 | C22 | semidirect |
| 21. C22×#3622 | C22 | semidirect |
| 22. #10587481 | C22 | semidirect |
| 23. #10587481 | C22 | semidirect |
| 24. #10587480 | C22 | semidirect |
| 25. #10587480 | C22 | semidirect |
| 26. #10587480 | C22 | semidirect |
| 38. #63252 | C2×C4 | semidirect |
| 41. C2×D68 | C2×C4 | semidirect |
| 95. #520 | D17 | semidirect |
| 117. #117 | C2×D17 | semidirect |
| 118. C2×C4⋊C4 | C2×D17 | semidirect |
| 124. C17 | #2897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587696 | 2 |
| C2×#10587634 | 2 |
| #11762813 | 2 |
| #11762808 | 2 |
| #11762803 | 2 |
| C2×#10587480 | 2 |
| C17×#520 | 2 |
| #2897 | 17 |