Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 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. #11763537 | C2 | semidirect |
| 3. #11763202 | C2 | semidirect |
| 5. #11763034 | C2 | semidirect |
| 6. #11763019 | C2 | semidirect |
| 7. #11763013 | C2 | semidirect |
| 9. #11762939 | C2 | semidirect |
| 10. #11762908 | C2 | semidirect |
| 11. C4×Q16×C17 | C2 | semidirect |
| 128. C4×Q16 | D17 | semidirect |
| 162. C17 | #3400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763544 | 2 |
| #11763537 | 2 |
| #11763202 | 2 |
| #11763182 | 2 |
| #11763034 | 2 |
| #11763019 | 2 |
| #11763013 | 2 |
| #11763009 | 2 |
| #11762939 | 2 |
| #11762908 | 2 |
| C4×Q16×C17 | 2 |
| #3400 | 17 |