Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
228 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 6. C22×#3624 | C4 | semidirect |
| 13. C22⋊#3624 | C4 | semidirect |
| 30. C22⋊C4×C17 | C8 | semidirect |
| 32. C22⋊Dic17 | C8 | semidirect |
| 108. C17 | #1282 | semidirect |
| 126. C22⋊C4 | #3624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#3624 | 2 |
| C22⋊C4×Dic17 | 2 |
| #1282 | 17 |