Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
888 conjugacy classes of subgroups; only the 354 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 354 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. #11763755 | C2 | direct (N × H) |
| 8. C2×C42×C17 | C4 | semidirect |
| 9. C2×C4×Dic17 | C4 | semidirect |
| 10. C42×D17 | C4 | semidirect |
| 22. C42×C17 | C2×C4 | semidirect |
| 23. C4×Dic17 | C2×C4 | semidirect |
| 31. C2×C4×C17 | C4⋊C4 | semidirect |
| 33. C2×Dic17 | C4⋊C4 | semidirect |
| 35. C4×D17 | C4⋊C4 | semidirect |
| 47. C4×C17 | C2×C4⋊C4 | semidirect |
| 48. Dic17 | C2×C4⋊C4 | semidirect |
| 52. C2×C17 | #384 | semidirect |
| 54. D17 | #384 | semidirect |
| 64. C2×C42 | #595 | semidirect |
| 65. C17 | C2×#384 | semidirect |
| 77. C42 | C2×#595 | semidirect |
| 90. C2×C4 | C4⋊#595 | semidirect |
| 101. C4 | C2×C4⋊#595 | semidirect |
| 105. C2 | #11763755 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#595 | 2 |
| #11763755 | 2 |
| C2×C42×D17 | 2 |
| C2×#384 | 17 |