Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
436 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10587555 | C2 | semidirect |
| 3. #11763169 | C2 | direct (N × H) |
| 4. C2×#10587487 | C2 | semidirect |
| 6. C2×C17×#97 | C2 | semidirect |
| 19. #10587555 | C22 | semidirect |
| 20. C17×#97 | C22 | semidirect |
| 22. #10587487 | C22 | semidirect |
| 88. C2×#97 | D17 | semidirect |
| 89. C2×C17 | #489 | semidirect |
| 109. #97 | C2×D17 | semidirect |
| 110. C17 | C2×#489 | semidirect |
| 171. C2 | #11763169 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587555 | 2 |
| C2×#10587561 | 2 |
| #11763169 | 2 |
| C2×#10587487 | 2 |
| C2×#10587492 | 2 |
| C2×C17×#97 | 2 |
| C2×#489 | 17 |