Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
392 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 91 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. C22×#63231 | C2 | semidirect |
| 4. C2×#10587487 | C2 | semidirect |
| 6. #11762571 | C2 | semidirect |
| 7. C2×C17×#103 | C2 | semidirect |
| 76. C22×D17 | Q16 | semidirect |
| 140. C2×#103 | D17 | semidirect |
| 172. C17 | #2001 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63231 | 2 |
| C2×#10587583 | 2 |
| C2×#10587632 | 2 |
| C2×#10587487 | 2 |
| C2×#10587491 | 2 |
| #11762571 | 2 |
| C2×C17×#103 | 2 |
| #2001 | 17 |