Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
3798 conjugacy classes of subgroups; only the 1179 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 1179 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. #14531961 | C2 | direct (N × H) |
| 2. C2×#11762689 | C2 | semidirect |
| 3. C2×#11762677 | C2 | semidirect |
| 7. #11762689 | C22 | semidirect |
| 8. #11762677 | C22 | semidirect |
| 11. C2×C17×#127 | C4 | semidirect |
| 17. C22×D4×C17 | C2×C4 | semidirect |
| 23. C17×#127 | C2×C4 | semidirect |
| 24. C2×C42×C17 | C2×C4 | semidirect |
| 37. C2×D4×C17 | C22×C4 | semidirect |
| 45. C42×C17 | C22×C4 | semidirect |
| 80. C2×#127 | Dic17 | semidirect |
| 88. C2×C17 | #2380 | semidirect |
| 94. C22×D4 | C2×Dic17 | semidirect |
| 100. #127 | C2×Dic17 | semidirect |
| 103. C2×C42 | C2×Dic17 | semidirect |
| 106. C17 | C2×#2380 | semidirect |
| 115. C2×D4 | C22×Dic17 | semidirect |
| 124. C42 | C22×Dic17 | semidirect |
| 152. C2 | #14531961 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531961 | 2 |
| C2×#11762689 | 2 |
| C2×#11762677 | 2 |
| C22×C17×#127 | 2 |
| C2×#2380 | 17 |