Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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×#10587637 | C2 | semidirect |
| 2. C2×M16×D17 | C2 | semidirect |
| 4. C2×#10587583 | C2 | semidirect |
| 5. #11763066 | C2 | semidirect |
| 6. #11763054 | C2 | semidirect |
| 7. #11763049 | C2 | semidirect |
| 8. #11763037 | C2 | semidirect |
| 9. #11762849 | C2 | semidirect |
| 10. #11762819 | C2 | semidirect |
| 11. C17×#417 | C2 | semidirect |
| 20. C2×#63231 | C22 | semidirect |
| 25. C2×#63229 | C22 | semidirect |
| 39. C17×#103 | C22 | semidirect |
| 40. C17×#102 | C22 | semidirect |
| 41. #10587487 | C22 | semidirect |
| 42. #10587487 | C22 | semidirect |
| 43. #10587479 | C22 | semidirect |
| 44. #10587478 | C22 | semidirect |
| 88. #63223 | D4 | semidirect |
| 146. C2×D17 | #137 | semidirect |
| 167. #417 | D17 | semidirect |
| 206. #103 | C2×D17 | semidirect |
| 207. #102 | C2×D17 | semidirect |
| 208. C17 | #3056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587637 | 2 |
| C2×M16×D17 | 2 |
| #11763316 | 2 |
| C2×#10587583 | 2 |
| #11763066 | 2 |
| #11763054 | 2 |
| #11763049 | 2 |
| #11763037 | 2 |
| #11762849 | 2 |
| #11762819 | 2 |
| C17×#417 | 2 |
| #3056 | 17 |