Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
326 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #11763214 | C2 | semidirect |
| 4. #11763207 | C2 | semidirect |
| 5. #11763160 | C2 | semidirect |
| 6. #11763160 | C2 | semidirect |
| 8. #11763117 | C2 | semidirect |
| 137. C17 | #3231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763366 | 2 |
| #11763214 | 2 |
| #11763207 | 2 |
| #11763160 | 2 |
| #11763151 | 2 |
| #11763117 | 2 |
| C17×#431 | 2 |
| #3231 | 17 |