Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
396 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 110 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. C4×#63242 | C2 | semidirect |
| 3. C4×C4⋊#595 | C2 | semidirect |
| 4. #11763682 | C2 | semidirect |
| 11. C4×D4×C17 | C4 | semidirect |
| 12. D4×Dic17 | C4 | semidirect |
| 14. #10587579 | C4 | semidirect |
| 18. C4×D68 | C4 | semidirect |
| 20. #10587547 | C4 | direct (N × H) |
| 43. C4⋊#595 | C2×C4 | semidirect |
| 46. #63242 | C2×C4 | semidirect |
| 69. D4×C17 | C42 | semidirect |
| 82. D68 | C42 | semidirect |
| 110. C4×C17 | #102 | semidirect |
| 115. Dic17 | #102 | semidirect |
| 137. C4×D4 | #595 | semidirect |
| 147. C17 | C4×#102 | semidirect |
| 193. D4 | C4×#595 | semidirect |
| 237. C4 | #10587547 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587547 | 2 |
| C4×#63242 | 2 |
| C4×C4⋊#595 | 2 |
| #11763682 | 2 |
| C4×D4×D17 | 2 |
| C4×#102 | 17 |