Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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. #11763095 | C2 | semidirect |
| 4. C8×Dic34 | C2 | semidirect |
| 5. #11762554 | C2 | semidirect |
| 7. C17×#334 | C2 | semidirect |
| 57. Dic34 | SD16 | semidirect |
| 61. C8×C17 | SD16 | semidirect |
| 80. #334 | D17 | semidirect |
| 102. C17 | #1666 | semidirect |
| 142. C8 | #63219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763182 | 2 |
| #11763095 | 2 |
| #11763010 | 2 |
| C8×Dic34 | 2 |
| #11762554 | 2 |
| #11762552 | 2 |
| C17×#334 | 2 |
| #1666 | 17 |