Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#63228 | C2 | semidirect |
| 2. C22×#63218 | C2 | semidirect |
| 3. C2×#10587581 | C2 | semidirect |
| 4. C2×#10587624 | C2 | semidirect |
| 5. #11763061 | C2 | direct (N × H) |
| 6. C2×#10587479 | C2 | semidirect |
| 7. C2×#10587492 | C2 | semidirect |
| 8. C2×C17×#102 | C2 | semidirect |
| 18. #10587624 | C22 | semidirect |
| 20. C2×#63228 | C22 | semidirect |
| 25. C2×#63218 | C22 | semidirect |
| 27. #10587581 | C22 | semidirect |
| 28. C17×#102 | C22 | semidirect |
| 29. #10587492 | C22 | semidirect |
| 30. #10587479 | C22 | semidirect |
| 63. C2×#3622 | D4 | semidirect |
| 101. #3622 | C2×D4 | semidirect |
| 132. C2×#102 | D17 | semidirect |
| 134. C2×C17 | #469 | semidirect |
| 161. #102 | C2×D17 | semidirect |
| 162. C17 | C2×#469 | semidirect |
| 259. C2 | #11763061 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63228 | 2 |
| C22×#63218 | 2 |
| C2×#10587581 | 2 |
| C2×#10587624 | 2 |
| #11763061 | 2 |
| C2×#10587479 | 2 |
| C2×#10587492 | 2 |
| C2×C17×#102 | 2 |
| C2×#469 | 17 |