Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#63230 | C2 | semidirect |
| 3. #11763283 | C2 | semidirect |
| 4. #11763021 | C2 | semidirect |
| 5. #11763011 | C2 | semidirect |
| 6. #11762836 | C2 | semidirect |
| 7. #11762818 | C2 | semidirect |
| 8. #11762805 | C2 | semidirect |
| 9. C17×#536 | C2 | semidirect |
| 13. C17×C4⋊Q8 | C22 | semidirect |
| 14. C17×#124 | C22 | semidirect |
| 29. #10587506 | C22 | semidirect |
| 30. #10587506 | C22 | semidirect |
| 31. #10587503 | C22 | semidirect |
| 32. C4⋊#3622 | C22 | semidirect |
| 114. #536 | D17 | semidirect |
| 136. C4⋊Q8 | C2×D17 | semidirect |
| 137. #124 | C2×D17 | semidirect |
| 149. C17 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587635 | 2 |
| C22×#63230 | 2 |
| #11763283 | 2 |
| #11763021 | 2 |
| #11763011 | 2 |
| #11762836 | 2 |
| #11762818 | 2 |
| #11762805 | 2 |
| C17×#536 | 2 |
| #3042 | 17 |