Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
388 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. C2×#10587532 | C2 | semidirect |
| 4. C4⋊C4×#595 | C2 | semidirect |
| 5. #11763683 | C2 | semidirect |
| 6. #11763682 | C2 | semidirect |
| 12. D4×#595 | C4 | semidirect |
| 20. #10587547 | C4 | semidirect |
| 23. C17×#102 | C4 | semidirect |
| 24. #10587503 | C4 | semidirect |
| 25. #10587492 | C4 | semidirect |
| 26. #10587480 | C4 | semidirect |
| 49. C4⋊#595 | C2×C4 | semidirect |
| 54. #63242 | C2×C4 | semidirect |
| 55. C2×C8×C17 | C2×C4 | semidirect |
| 56. C4⋊C4×C17 | C2×C4 | semidirect |
| 57. C4⋊Dic17 | C2×C4 | semidirect |
| 59. C2×#3622 | C2×C4 | semidirect |
| 85. D4×C17 | C42 | semidirect |
| 93. D68 | C42 | semidirect |
| 163. #102 | #595 | semidirect |
| 166. C17 | #1762 | semidirect |
| 190. C2×C8 | C2×#595 | semidirect |
| 197. C4⋊C4 | C2×#595 | semidirect |
| 216. D4 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#595 | 2 |
| C2×#10587547 | 2 |
| C2×#10587532 | 2 |
| C4⋊C4×#595 | 2 |
| #11763683 | 2 |
| #11763682 | 2 |
| #102×D17 | 2 |
| #1762 | 17 |