Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
598 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#10587477 | C2 | semidirect |
| 3. #11762665 | C2 | semidirect |
| 4. #11762575 | C2 | semidirect |
| 5. C22×C22⋊C4×C17 | C2 | semidirect |
| 8. C22×C22⋊D17 | C4 | semidirect |
| 17. C2×C22⋊Dic17 | C4 | semidirect |
| 29. C23×D17 | C2×C4 | semidirect |
| 41. C22×Dic17 | C2×C4 | semidirect |
| 42. C22×Dic17 | C2×C4 | semidirect |
| 45. C22⋊C4×C17 | D4 | semidirect |
| 109. C22×C17 | #99 | semidirect |
| 123. C22×C22⋊C4 | D17 | semidirect |
| 151. C17 | #1898 | semidirect |
| 183. C22⋊C4 | C22⋊D17 | semidirect |
| 242. C22 | #10587477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587639 | 2 |
| C2×#10587477 | 2 |
| #11762665 | 2 |
| #11762575 | 2 |
| C22×C22⋊C4×C17 | 2 |
| #1898 | 17 |