Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
474 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 1. C22×#63219 | C2 | semidirect |
| 2. C22×#63229 | C2 | semidirect |
| 4. C2×#10587480 | C2 | semidirect |
| 5. #11762714 | C2 | semidirect |
| 6. #11762563 | C2 | semidirect |
| 7. C2×C17×#102 | C2 | semidirect |
| 53. C2×Dic34 | D4 | semidirect |
| 56. C2×C8×C17 | D4 | semidirect |
| 64. C2×#3622 | D4 | semidirect |
| 95. C2×Dic17 | SD16 | semidirect |
| 133. C2×#102 | D17 | semidirect |
| 162. C17 | #2014 | semidirect |
| 197. C2×C8 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63219 | 2 |
| C22×#63229 | 2 |
| C2×#10587626 | 2 |
| C2×#10587480 | 2 |
| #11762714 | 2 |
| #11762563 | 2 |
| C2×C17×#102 | 2 |
| #2014 | 17 |