Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
264 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 8. C22⋊#3624 | C4 | semidirect |
| 12. C17×C22⋊C8 | C4 | semidirect |
| 13. C22⋊#3622 | C4 | semidirect |
| 20. C22×#595 | C8 | semidirect |
| 100. C22⋊C8 | #595 | semidirect |
| 103. C17 | #1280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763777 | 2 |
| C2×(C2×#595)⋊C4 | 2 |
| C22⋊C8×D17 | 2 |
| #1280 | 17 |