Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
406 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 99 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×#10587506 | C2 | semidirect |
| 4. #11762564 | C2 | semidirect |
| 5. C2×C17×C4⋊Q8 | C2 | semidirect |
| 56. C2×C4×C17 | SD16 | semidirect |
| 83. C2×C4⋊Q8 | D17 | semidirect |
| 105. C17 | #2013 | semidirect |
| 148. C2×C4 | #63230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63230 | 2 |
| C2×#10587506 | 2 |
| #11762711 | 2 |
| #11762564 | 2 |
| C2×C17×C4⋊Q8 | 2 |
| #2013 | 17 |