Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
456 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 177 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×#10587593 | C2 | semidirect |
| 3. #11762930 | C2 | semidirect |
| 4. #11762925 | C2 | semidirect |
| 5. #11762825 | C2 | semidirect |
| 6. #11762767 | C2 | semidirect |
| 7. C17×#430 | C2 | semidirect |
| 13. #10587595 | C4 | semidirect |
| 14. #10587594 | C4 | semidirect |
| 17. #10587593 | C22 | semidirect |
| 18. #10587593 | C22 | semidirect |
| 22. C17×#108 | C22 | semidirect |
| 23. #10587496 | C22 | semidirect |
| 24. #10587486 | C22 | semidirect |
| 25. C8×Dic17 | C22 | semidirect |
| 90. #430 | D17 | semidirect |
| 111. #108 | C2×D17 | semidirect |
| 115. C17 | #2955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763609 | 2 |
| C2×#10587593 | 2 |
| #11762930 | 2 |
| #11762925 | 2 |
| #11762825 | 2 |
| #11762767 | 2 |
| C17×#430 | 2 |
| #2955 | 17 |