Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
392 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 392 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. Q8×Dic34 | C2 | semidirect |
| 3. #11763156 | C2 | semidirect |
| 4. #11763100 | C2 | semidirect |
| 5. #11763010 | C2 | semidirect |
| 6. C4×#63219 | C2 | semidirect |
| 7. C8×Q8×C17 | C2 | semidirect |
| 44. Q8×C17 | SD16 | semidirect |
| 58. Dic34 | #41 | semidirect |
| 78. C8×Q8 | D17 | semidirect |
| 100. C17 | #3362 | semidirect |
| 124. Q8 | #63219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic34 | 2 |
| #11763481 | 2 |
| #11763156 | 2 |
| #11763100 | 2 |
| #11763010 | 2 |
| C4×#63219 | 2 |
| C8×Q8×C17 | 2 |
| #3362 | 17 |