Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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×#63219 | C2 | semidirect |
| 3. #11763380 | C2 | semidirect |
| 4. #11763283 | C2 | semidirect |
| 5. #11763023 | C2 | semidirect |
| 6. #11763013 | C2 | semidirect |
| 7. #11762835 | C2 | semidirect |
| 8. #11762817 | C2 | semidirect |
| 9. C17×#416 | C2 | semidirect |
| 16. #10587630 | C22 | semidirect |
| 18. #10587622 | C22 | semidirect |
| 29. C17×#103 | C22 | semidirect |
| 30. C17×#102 | C22 | semidirect |
| 31. #10587485 | C22 | semidirect |
| 32. #10587481 | C22 | semidirect |
| 120. #416 | D17 | semidirect |
| 147. #103 | C2×D17 | semidirect |
| 148. #102 | 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×#63219 | 2 |
| #11763380 | 2 |
| #11763283 | 2 |
| #11763023 | 2 |
| #11763013 | 2 |
| #11762835 | 2 |
| #11762817 | 2 |
| C17×#416 | 2 |
| #3042 | 17 |