Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
442 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 76 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. C22×C4×#595 | C2 | semidirect |
| 2. C2×#10587548 | C2 | semidirect |
| 3. #11763780 | C2 | semidirect |
| 4. #11763679 | C2 | semidirect |
| 13. C17×#121 | C4 | semidirect |
| 14. #10587624 | C4 | semidirect |
| 17. #10587610 | C4 | semidirect |
| 18. #10587583 | C4 | semidirect |
| 31. C2×D4×C17 | C2×C4 | semidirect |
| 45. C2×Dic34 | C2×C4 | semidirect |
| 49. C4×#595 | D4 | semidirect |
| 52. C4⋊C4×C17 | C2×C4 | semidirect |
| 59. C4⋊Dic17 | C2×C4 | semidirect |
| 103. C22×C17 | #104 | semidirect |
| 111. C2×D17 | #104 | semidirect |
| 143. #121 | #595 | semidirect |
| 154. C17 | #1896 | semidirect |
| 162. C2×D4 | C2×#595 | semidirect |
| 182. C4⋊C4 | C2×#595 | semidirect |
| 241. C22 | #10587548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#595 | 2 |
| C2×#10587548 | 2 |
| #11763780 | 2 |
| #11763679 | 2 |
| #11763319 | 2 |
| #1896 | 17 |