Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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. #11763157 | C2 | semidirect |
| 2. #11763096 | C2 | semidirect |
| 4. #11762886 | C2 | semidirect |
| 5. #11762561 | C2 | semidirect |
| 6. #11762552 | C2 | semidirect |
| 7. C17×#333 | C2 | semidirect |
| 83. #333 | D17 | semidirect |
| 105. C17 | #1697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763157 | 2 |
| #11763096 | 2 |
| #11763005 | 2 |
| #11762886 | 2 |
| #11762561 | 2 |
| #11762552 | 2 |
| C17×#333 | 2 |
| #1697 | 17 |