Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
262 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 66 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. #11763824 | C2 | semidirect |
| 3. #11763813 | C2 | semidirect |
| 5. #11763692 | C2 | semidirect |
| 6. #11763680 | C2 | semidirect |
| 25. C17×#104 | C4 | semidirect |
| 26. #10587508 | C4 | semidirect |
| 27. #10587496 | C4 | semidirect |
| 28. #10587476 | C4 | semidirect |
| 148. #104 | #595 | semidirect |
| 149. C17 | #1861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763888 | 2 |
| #11763824 | 2 |
| #11763813 | 2 |
| #11763806 | 2 |
| #11763692 | 2 |
| #11763680 | 2 |
| #104×D17 | 2 |
| #1861 | 17 |