Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
11422 conjugacy classes of subgroups; only the 5752 normal subgroups are shown.
This group has 11422 conjugacy classes of subgroups — too many to draw. Only its 5752 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×#10587680 | C2 | direct (N × H) |
| 2. C23×#63243 | C2 | semidirect |
| 3. C23×#63242 | C2 | semidirect |
| 5. C2×#10587680 | C22 | direct (N × H) |
| 6. C22×#63243 | C22 | semidirect |
| 7. C22×#63242 | C22 | semidirect |
| 26. #10587680 | C23 | direct (N × H) |
| 27. C2×#63243 | C23 | semidirect |
| 28. C2×#63242 | C23 | semidirect |
| 43. #63243 | C24 | semidirect |
| 44. #63242 | C24 | semidirect |
| 46. C23×C17 | #131 | semidirect |
| 63. C22×C17 | C2×#131 | semidirect |
| 80. C2×C17 | C22×#131 | semidirect |
| 97. C17 | C23×#131 | semidirect |
| 116. C23 | #10587680 | direct (N × H) |
| 129. C22 | C2×#10587680 | direct (N × H) |
| 135. C2 | C22×#10587680 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587680 | 2 |
| C23×#63243 | 2 |
| C23×#63242 | 2 |
| C23×#63256 | 2 |
| C23×#131 | 17 |