Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
402 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 1. #11763387 | C2 | semidirect |
| 2. #11763145 | C2 | semidirect |
| 3. #11763123 | C2 | semidirect |
| 4. #11763055 | C2 | semidirect |
| 5. #11763050 | C2 | semidirect |
| 6. #11763045 | C2 | semidirect |
| 7. #11762973 | C2 | semidirect |
| 8. #11762956 | C2 | semidirect |
| 9. C17×#408 | C2 | semidirect |
| 122. #408 | D17 | semidirect |
| 154. C17 | #3203 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763387 | 2 |
| #11763145 | 2 |
| #11763123 | 2 |
| #11763055 | 2 |
| #11763050 | 2 |
| #11763045 | 2 |
| #11762973 | 2 |
| #11762956 | 2 |
| C17×#408 | 2 |
| #3203 | 17 |