Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
736 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 218 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 |
|---|---|---|
| 2. C2×#10587545 | C2 | direct (N × H) |
| 14. #10587545 | C22 | direct (N × H) |
| 57. C22×C17 | #101 | semidirect |
| 70. C2×C17 | C2×#101 | semidirect |
| 83. C17 | C22×#101 | semidirect |
| 125. C22 | #10587545 | direct (N × H) |
| 135. C2 | C2×#10587545 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63247 | 2 |
| C2×#10587545 | 2 |
| C23×Dic34 | 2 |
| C22×#101 | 17 |