Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
160 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 90 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. C2×#63216 | C4 | semidirect |
| 25. C2×C4×C17 | C16 | semidirect |
| 60. C17 | #1374 | semidirect |
| 76. C2×C4 | #63216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63216 | 2 |
| C2×C4×#3622 | 2 |
| #1374 | 17 |