Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
412 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 112 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. C2×#10587532 | C2 | semidirect |
| 4. #11763674 | C2 | semidirect |
| 14. C22⋊#3624 | C4 | semidirect |
| 15. #10587543 | C4 | semidirect |
| 17. C17×C22⋊C8 | C4 | semidirect |
| 18. C22⋊#3622 | C4 | semidirect |
| 19. #10587491 | C4 | semidirect |
| 34. C2×#3624 | C2×C4 | semidirect |
| 40. C2×C8×C17 | C2×C4 | semidirect |
| 41. C2×#3622 | C2×C4 | semidirect |
| 76. C22×C17 | #97 | semidirect |
| 82. C2×D17 | #97 | semidirect |
| 117. C22⋊C8 | #595 | semidirect |
| 119. C17 | #1749 | semidirect |
| 140. C2×C8 | C2×#595 | semidirect |
| 184. C22 | #10587532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#595 | 2 |
| #11763777 | 2 |
| C2×#10587532 | 2 |
| #11763674 | 2 |
| C22⋊C8×D17 | 2 |
| #1749 | 17 |