Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
2830 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2830 conjugacy classes of subgroups — too many to draw. Only its 747 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×#10587556 | C2 | semidirect |
| 3. C2×#11763174 | C2 | direct (N × H) |
| 4. C22×#10587492 | C2 | semidirect |
| 5. C22×C17×#97 | C2 | semidirect |
| 11. C2×#10587556 | C22 | semidirect |
| 14. #11763174 | C22 | direct (N × H) |
| 15. C2×#10587492 | C22 | semidirect |
| 18. C2×C17×#97 | C22 | semidirect |
| 38. #10587556 | C23 | semidirect |
| 39. C17×#97 | C23 | semidirect |
| 40. #10587492 | C23 | semidirect |
| 89. C22×#97 | D17 | semidirect |
| 90. C22×C17 | #490 | semidirect |
| 113. C2×#97 | C2×D17 | semidirect |
| 114. C2×C17 | C2×#490 | semidirect |
| 139. #97 | C22×D17 | semidirect |
| 140. C17 | C22×#490 | semidirect |
| 187. C22 | #11763174 | direct (N × H) |
| 196. C2 | C2×#11763174 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587560 | 2 |
| C22×#10587556 | 2 |
| C2×#11763174 | 2 |
| C22×#10587492 | 2 |
| C22×C17×#97 | 2 |
| C22×#490 | 17 |