Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1880 conjugacy classes of subgroups; only the 810 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 810 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×#10587677 | C2 | direct (N × H) |
| 2. C22×C4⋊#595 | C2 | semidirect |
| 4. C22×C4×#595 | C2 | semidirect |
| 8. C23×C4×C17 | C4 | semidirect |
| 9. C23×Dic17 | C4 | semidirect |
| 10. C22×C4×D17 | C4 | semidirect |
| 11. C22×C4×D17 | C4 | semidirect |
| 12. C22×C4×D17 | C4 | semidirect |
| 17. #10587677 | C22 | direct (N × H) |
| 18. C2×C4⋊#595 | C22 | semidirect |
| 19. C2×C4×#595 | C22 | semidirect |
| 30. C22×C4×C17 | C2×C4 | semidirect |
| 33. C22×Dic17 | C2×C4 | semidirect |
| 36. C2×C4×D17 | C2×C4 | semidirect |
| 37. C2×C4×D17 | C2×C4 | semidirect |
| 38. C2×C4×D17 | C2×C4 | semidirect |
| 43. C4⋊#595 | C23 | semidirect |
| 44. C4×#595 | C23 | semidirect |
| 61. C2×C4×C17 | C22×C4 | semidirect |
| 64. C2×Dic17 | C22×C4 | semidirect |
| 67. C4×D17 | C22×C4 | semidirect |
| 68. C4×D17 | C22×C4 | semidirect |
| 73. C22×C17 | #117 | semidirect |
| 79. C2×D17 | #117 | semidirect |
| 95. C2×C17 | C2×#117 | semidirect |
| 98. D17 | C2×#117 | semidirect |
| 109. C23×C4 | #595 | semidirect |
| 114. C17 | C22×#117 | semidirect |
| 136. C22×C4 | C2×#595 | semidirect |
| 165. C2×C4 | C22×#595 | semidirect |
| 175. C22 | #10587677 | direct (N × H) |
| 187. C2 | C2×#10587677 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587677 | 2 |
| C22×C4⋊#595 | 2 |
| C22×C22⋊#595 | 2 |
| C22×C4×#595 | 2 |
| C23×C4×D17 | 2 |
| C22×#117 | 17 |