Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11763519 | C2 | semidirect |
| 2. #11763481 | C2 | semidirect |
| 3. #11763174 | C2 | semidirect |
| 4. #11763156 | C2 | semidirect |
| 5. #11763110 | C2 | semidirect |
| 6. #11763100 | C2 | semidirect |
| 7. #11763005 | C2 | semidirect |
| 8. #11763005 | C2 | semidirect |
| 9. #11762922 | C2 | semidirect |
| 10. C4×D136 | C2 | semidirect |
| 11. C17×#446 | C2 | semidirect |
| 95. D68 | #41 | semidirect |
| 132. #446 | D17 | semidirect |
| 170. C17 | #3366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763519 | 2 |
| #11763481 | 2 |
| #11763174 | 2 |
| #11763156 | 2 |
| #11763110 | 2 |
| #11763100 | 2 |
| #11763005 | 2 |
| #11762922 | 2 |
| C4×D136 | 2 |
| C17×#446 | 2 |
| #3366 | 17 |