Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1144 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1144 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 |
|---|---|---|
| 2. #11763752 | C2 | direct (N × H) |
| 3. C2×(C2×#595)⋊C4 | C2 | semidirect |
| 7. C23×C4×C17 | C4 | semidirect |
| 8. C23×Dic17 | C4 | semidirect |
| 10. C22×C4×D17 | C4 | semidirect |
| 11. C22×C4×D17 | C4 | semidirect |
| 16. (C2×#595)⋊C4 | C22 | semidirect |
| 29. C22×C4×C17 | C2×C4 | semidirect |
| 32. C22×Dic17 | C2×C4 | semidirect |
| 38. C2×C4×D17 | C2×C4 | semidirect |
| 94. C2×C17 | #381 | semidirect |
| 98. D17 | #381 | semidirect |
| 108. C23×C4 | #595 | semidirect |
| 112. C17 | C2×#381 | semidirect |
| 135. C22×C4 | C2×#595 | semidirect |
| 188. C2 | #11763752 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#595 | 2 |
| #11763752 | 2 |
| C2×(C2×#595)⋊C4 | 2 |
| C23×C4×D17 | 2 |
| C2×#381 | 17 |