Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1072 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 258 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×#63242 | C2 | semidirect |
| 2. C22×C4⋊#595 | C2 | semidirect |
| 3. C2×#10587547 | C2 | direct (N × H) |
| 7. C22×D4×C17 | C4 | semidirect |
| 11. C2×D4×D17 | C4 | semidirect |
| 13. C22×D68 | C4 | semidirect |
| 17. C2×C4⋊#595 | C22 | semidirect |
| 19. C2×#63242 | C22 | semidirect |
| 20. #10587547 | C22 | direct (N × H) |
| 31. C2×D4×C17 | C2×C4 | semidirect |
| 39. D4×D17 | C2×C4 | semidirect |
| 42. C2×D68 | C2×C4 | semidirect |
| 49. C4⋊#595 | C23 | semidirect |
| 51. #63242 | C23 | semidirect |
| 69. D4×C17 | C22×C4 | semidirect |
| 77. D68 | C22×C4 | semidirect |
| 87. C22×C17 | #102 | semidirect |
| 94. C2×D17 | #102 | semidirect |
| 109. C2×C17 | C2×#102 | semidirect |
| 112. D17 | C2×#102 | semidirect |
| 122. C22×D4 | #595 | semidirect |
| 131. C17 | C22×#102 | semidirect |
| 149. C2×D4 | C2×#595 | semidirect |
| 182. D4 | C22×#595 | semidirect |
| 207. C22 | #10587547 | direct (N × H) |
| 219. C2 | C2×#10587547 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63242 | 2 |
| C22×C4⋊#595 | 2 |
| C2×#10587547 | 2 |
| C22×D4×D17 | 2 |
| C22×#102 | 17 |