Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 88 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. C2×#10587533 | C2 | semidirect |
| 4. #11763683 | C2 | semidirect |
| 17. C17×C22⋊C8 | C4 | semidirect |
| 18. C22⋊#3622 | C4 | semidirect |
| 19. #10587491 | C4 | semidirect |
| 41. C2×C8×C17 | C2×C4 | semidirect |
| 42. C2×#3622 | C2×C4 | semidirect |
| 81. C22×C17 | #106 | semidirect |
| 89. C2×D17 | #106 | semidirect |
| 129. C22⋊C8 | #595 | semidirect |
| 131. C17 | #1853 | semidirect |
| 150. C2×C8 | C2×#595 | semidirect |
| 205. C22 | #10587533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#595 | 2 |
| C2×#10587533 | 2 |
| #11763751 | 2 |
| #11763683 | 2 |
| C22⋊C8×D17 | 2 |
| #1853 | 17 |