Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic34 | C2 | semidirect |
| 3. #11763160 | C2 | semidirect |
| 4. #11763140 | C2 | semidirect |
| 5. #11763095 | C2 | semidirect |
| 6. #11763038 | C2 | semidirect |
| 7. #11763015 | C2 | semidirect |
| 8. #11762950 | C2 | semidirect |
| 9. C4×#63219 | C2 | semidirect |
| 10. C2×#10587487 | C2 | semidirect |
| 11. C8×D4×C17 | C2 | semidirect |
| 79. D4×C17 | SD16 | semidirect |
| 102. Dic34 | #41 | semidirect |
| 133. C8×D4 | D17 | semidirect |
| 169. C17 | #3298 | semidirect |
| 217. D4 | #63219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic34 | 2 |
| #11763463 | 2 |
| #11763160 | 2 |
| #11763140 | 2 |
| #11763095 | 2 |
| #11763038 | 2 |
| #11763015 | 2 |
| #11762950 | 2 |
| C4×#63219 | 2 |
| C2×#10587487 | 2 |
| C8×D4×C17 | 2 |
| #3298 | 17 |