Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. C4×C4⋊Dic17 | C2 | semidirect |
| 4. #11762570 | C2 | semidirect |
| 5. C17×#423 | C2 | semidirect |
| 14. C4×D68 | C4 | semidirect |
| 15. C4×D68 | C4 | semidirect |
| 18. C4×Dic34 | C4 | semidirect |
| 19. C4×Dic34 | C4 | semidirect |
| 81. D68 | C4⋊C4 | semidirect |
| 87. Dic34 | C4⋊C4 | semidirect |
| 101. C4×C17 | #104 | semidirect |
| 111. #423 | D17 | semidirect |
| 139. C17 | #1806 | semidirect |
| 220. C4 | #10587496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#63252 | 2 |
| C2×#10587496 | 2 |
| C4×C4⋊Dic17 | 2 |
| #11762570 | 2 |
| C17×#423 | 2 |
| #1806 | 17 |