Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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×M16×D17 | C2 | semidirect |
| 3. C2×#10587632 | C2 | semidirect |
| 4. #11763064 | C2 | semidirect |
| 5. #11763052 | C2 | semidirect |
| 6. #11763047 | C2 | semidirect |
| 7. #11763035 | C2 | semidirect |
| 8. #11762851 | C2 | semidirect |
| 9. #11762818 | C2 | semidirect |
| 10. #11762810 | C2 | semidirect |
| 11. C2×C17×#137 | C2 | semidirect |
| 16. C2×Q16×C17 | C22 | semidirect |
| 17. C2×SD16×C17 | C22 | semidirect |
| 39. #10587506 | C22 | semidirect |
| 40. #10587506 | C22 | semidirect |
| 41. #10587506 | C22 | semidirect |
| 42. #10587503 | C22 | semidirect |
| 43. #10587489 | C22 | semidirect |
| 44. #10587488 | C22 | semidirect |
| 70. M16×C17 | D4 | semidirect |
| 146. C2×D17 | #137 | semidirect |
| 157. C2×#137 | D17 | semidirect |
| 179. C2×Q16 | C2×D17 | semidirect |
| 180. C2×SD16 | C2×D17 | semidirect |
| 208. C17 | #3056 | semidirect |
| 236. M16 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D17 | 2 |
| #11763316 | 2 |
| C2×#10587632 | 2 |
| #11763064 | 2 |
| #11763052 | 2 |
| #11763047 | 2 |
| #11763035 | 2 |
| #11762851 | 2 |
| #11762818 | 2 |
| #11762810 | 2 |
| C2×C17×#137 | 2 |
| #3056 | 17 |