Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
336 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 98 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. C2×C8×#595 | C2 | semidirect |
| 5. #11763674 | C2 | semidirect |
| 6. #11763674 | C2 | semidirect |
| 19. C22⋊#3624 | C4 | semidirect |
| 20. #10587543 | C4 | semidirect |
| 23. C17×C22⋊C8 | C4 | semidirect |
| 24. C22⋊#3622 | C4 | semidirect |
| 25. #10587491 | C4 | semidirect |
| 26. #10587491 | C4 | semidirect |
| 149. C22⋊C8 | #595 | semidirect |
| 152. C17 | #1750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587677 | 2 |
| #11763777 | 2 |
| C2×#10587532 | 2 |
| C2×C8×#595 | 2 |
| #11763674 | 2 |
| C22⋊C8×D17 | 2 |
| #1750 | 17 |