Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 197 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. #11762863 | C2 | semidirect |
| 3. #11762859 | C2 | semidirect |
| 4. #11762832 | C2 | semidirect |
| 6. M16×Dic17 | C2 | semidirect |
| 21. #10587486 | C22 | semidirect |
| 22. #10587485 | C22 | semidirect |
| 23. C8×Dic17 | C22 | semidirect |
| 67. C2×Dic17 | M16 | semidirect |
| 116. C17 | #2920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic17 | 2 |
| #11762863 | 2 |
| #11762859 | 2 |
| #11762832 | 2 |
| #11762773 | 2 |
| M16×Dic17 | 2 |
| C17×#407 | 2 |
| #2920 | 17 |