Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. Q8×D68 | C2 | semidirect |
| 3. #11763160 | C2 | semidirect |
| 4. #11763153 | C2 | semidirect |
| 5. #11763104 | C2 | semidirect |
| 6. #11763054 | C2 | semidirect |
| 7. #11763014 | C2 | semidirect |
| 8. #11762946 | C2 | semidirect |
| 9. #11762888 | C2 | semidirect |
| 10. #11762816 | C2 | semidirect |
| 11. C4×SD16×C17 | C2 | semidirect |
| 130. C4×SD16 | D17 | semidirect |
| 167. C17 | #3329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763524 | 2 |
| Q8×D68 | 2 |
| #11763160 | 2 |
| #11763153 | 2 |
| #11763104 | 2 |
| #11763054 | 2 |
| #11763014 | 2 |
| #11762946 | 2 |
| #11762888 | 2 |
| #11762816 | 2 |
| C4×SD16×C17 | 2 |
| #3329 | 17 |