Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
324 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 5. C22×Q8×C17 | C4 | semidirect |
| 16. C2×C4⋊Dic17 | C4 | semidirect |
| 17. C2×#63225 | C4 | semidirect |
| 37. C22⋊#595 | Q8 | semidirect |
| 108. C22×Q8 | #595 | semidirect |
| 123. C17 | #1996 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763751 | 2 |
| C4×C22⋊#595 | 2 |
| #11763687 | 2 |
| C2×#10587632 | 2 |
| #1996 | 17 |