Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #11763101 | C2 | semidirect |
| 4. #11763016 | C2 | semidirect |
| 6. C4×#63231 | C2 | semidirect |
| 70. C2×C4×C17 | Q16 | semidirect |
| 136. C17 | #3104 | semidirect |
| 181. C2×C4 | #63231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic34 | 2 |
| #11763142 | 2 |
| #11763101 | 2 |
| #11763016 | 2 |
| #11762964 | 2 |
| C4×#63231 | 2 |
| #11762862 | 2 |
| C17×#533 | 2 |
| #3104 | 17 |