Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
740 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×Dic68 | C2 | semidirect |
| 3. C22×#63231 | C2 | semidirect |
| 5. #11762966 | C2 | direct (N × H) |
| 6. C2×#10587481 | C2 | semidirect |
| 8. C2×C17×#103 | C2 | semidirect |
| 22. C2×#63231 | C22 | semidirect |
| 27. C2×Dic68 | C22 | semidirect |
| 30. C17×#103 | C22 | semidirect |
| 32. #10587481 | C22 | semidirect |
| 76. C22×D17 | Q16 | semidirect |
| 116. C2×D17 | C2×Q16 | semidirect |
| 131. C2×#103 | D17 | semidirect |
| 133. C2×C17 | #451 | semidirect |
| 160. #103 | C2×D17 | semidirect |
| 162. C17 | C2×#451 | semidirect |
| 255. C2 | #11762966 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D17 | 2 |
| C22×Dic68 | 2 |
| C22×#63231 | 2 |
| C2×#10587583 | 2 |
| #11762966 | 2 |
| C2×#10587481 | 2 |
| C2×#10587491 | 2 |
| C2×C17×#103 | 2 |
| C2×#451 | 17 |