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 |
|---|---|---|
| 1. #11763091 | C2 | semidirect |
| 3. C8×Dic34 | C2 | semidirect |
| 4. #11762560 | C2 | semidirect |
| 5. #11762555 | C2 | semidirect |
| 57. Dic34 | SD16 | semidirect |
| 59. C8×C17 | SD16 | semidirect |
| 102. C17 | #1666 | semidirect |
| 142. C8 | #63229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763091 | 2 |
| #11763006 | 2 |
| C8×Dic34 | 2 |
| #11762560 | 2 |
| #11762555 | 2 |
| #11762553 | 2 |
| C17×#492 | 2 |
| #1666 | 17 |