Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#10587593 | C2 | semidirect |
| 3. #11763383 | C2 | semidirect |
| 4. #11763064 | C2 | semidirect |
| 5. #11763052 | C2 | semidirect |
| 6. #11763047 | C2 | semidirect |
| 7. #11763035 | C2 | semidirect |
| 8. #11762851 | C2 | semidirect |
| 9. #11762805 | C2 | semidirect |
| 10. C2×#10587506 | C2 | semidirect |
| 11. C2×C17×#137 | C2 | semidirect |
| 65. M16×C17 | D4 | semidirect |
| 138. C2×#137 | D17 | semidirect |
| 186. C17 | #3063 | semidirect |
| 210. M16 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587593 | 2 |
| #11763387 | 2 |
| #11763383 | 2 |
| #11763064 | 2 |
| #11763052 | 2 |
| #11763047 | 2 |
| #11763035 | 2 |
| #11762851 | 2 |
| #11762805 | 2 |
| C2×#10587506 | 2 |
| C2×C17×#137 | 2 |
| #3063 | 17 |