Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
5838 conjugacy classes of subgroups; only the 1339 normal subgroups are shown.
This group has 5838 conjugacy classes of subgroups — too many to draw. Only its 1339 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. C23×#63225 | C2 | semidirect |
| 3. C2×#11762733 | C2 | direct (N × H) |
| 4. C22×C17×#95 | C2 | semidirect |
| 8. C22×#63225 | C22 | semidirect |
| 11. #11762733 | C22 | direct (N × H) |
| 13. C2×C17×#95 | C22 | semidirect |
| 30. C2×#63225 | C23 | semidirect |
| 31. C17×#95 | C23 | semidirect |
| 81. C22×#95 | D17 | semidirect |
| 82. C22×C17 | #396 | semidirect |
| 103. C2×#95 | C2×D17 | semidirect |
| 104. C2×C17 | C2×#396 | semidirect |
| 126. #95 | C22×D17 | semidirect |
| 127. C17 | C22×#396 | semidirect |
| 177. C22 | #11762733 | direct (N × H) |
| 187. C2 | C2×#11762733 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#63225 | 2 |
| C23×#63227 | 2 |
| C2×#11762733 | 2 |
| C22×C17×#95 | 2 |
| C22×#396 | 17 |