Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
254 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 20. #10587481 | C4 | semidirect |
| 127. C17 | #1927 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587479 | 2 |
| C2×#10587481 | 2 |
| #11762715 | 2 |
| #11762571 | 2 |
| #11762564 | 2 |
| C4×C4⋊C4×C17 | 2 |
| #1927 | 17 |