Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
228 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 56 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×C8×C17 | C4 | semidirect |
| 7. C22×#3622 | C4 | semidirect |
| 8. (C2×#595)⋊C4 | C4 | semidirect |
| 76. C22×C8 | #595 | semidirect |
| 81. C17 | #1289 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763751 | 2 |
| C2×#10587491 | 2 |
| #1289 | 17 |