Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 21. C17×C4⋊C8 | C4 | semidirect |
| 22. #10587485 | C4 | semidirect |
| 23. #10587485 | C4 | semidirect |
| 24. C4⋊#3622 | C4 | semidirect |
| 131. C4⋊C8 | #595 | semidirect |
| 135. C17 | #1949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587534 | 2 |
| C2×#10587533 | 2 |
| #11763753 | 2 |
| C4×C4⋊#595 | 2 |
| #11763683 | 2 |
| C4⋊C8×D17 | 2 |
| #1949 | 17 |