Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 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. #11763365 | C2 | semidirect |
| 3. #11763177 | C2 | semidirect |
| 4. #11763175 | C2 | semidirect |
| 5. #11763174 | C2 | semidirect |
| 6. #11763170 | C2 | semidirect |
| 7. #11762804 | C2 | semidirect |
| 8. #97×D17 | C2 | semidirect |
| 9. C17×#491 | C2 | semidirect |
| 90. #491 | D17 | semidirect |
| 121. C17 | #3135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763365 | 2 |
| #11763360 | 2 |
| #11763177 | 2 |
| #11763175 | 2 |
| #11763174 | 2 |
| #11763170 | 2 |
| #11762804 | 2 |
| #97×D17 | 2 |
| C17×#491 | 2 |
| #3135 | 17 |