Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
436 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 436 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×#10587574 | C2 | semidirect |
| 3. #11763170 | C2 | direct (N × H) |
| 4. C2×#10587506 | C2 | semidirect |
| 7. C2×#10587486 | C2 | semidirect |
| 8. C2×C17×#103 | C2 | semidirect |
| 23. #10587574 | C22 | semidirect |
| 24. C17×#103 | C22 | semidirect |
| 25. #10587506 | C22 | semidirect |
| 27. #10587486 | C22 | semidirect |
| 108. C2×#103 | D17 | semidirect |
| 112. C2×C17 | #489 | semidirect |
| 133. #103 | C2×D17 | semidirect |
| 137. C17 | C2×#489 | semidirect |
| 213. C2 | #11763170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587574 | 2 |
| C2×#10587633 | 2 |
| #11763170 | 2 |
| C2×#10587506 | 2 |
| C2×#10587492 | 2 |
| C2×#10587480 | 2 |
| C2×#10587486 | 2 |
| C2×C17×#103 | 2 |
| C2×#489 | 17 |