Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
338 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11763538 | C2 | semidirect |
| 3. #11763209 | C2 | semidirect |
| 4. #11763207 | C2 | semidirect |
| 5. #11763114 | C2 | semidirect |
| 7. #11763104 | C2 | semidirect |
| 9. C8×Dic34 | C2 | semidirect |
| 48. SD16×C17 | Q8 | semidirect |
| 155. C17 | #3381 | semidirect |
| 163. SD16 | Dic34 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763538 | 2 |
| #11763516 | 2 |
| #11763209 | 2 |
| #11763207 | 2 |
| #11763114 | 2 |
| #11763111 | 2 |
| #11763104 | 2 |
| #11763089 | 2 |
| C8×Dic34 | 2 |
| SD16×Dic17 | 2 |
| C4×SD16×C17 | 2 |
| #3381 | 17 |