Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
298 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 3. #14545804 | C2 | semidirect |
| 4. #14545803 | C2 | semidirect |
| 28. #10587538 | C8 | semidirect |
| 33. #10587530 | C8 | semidirect |
| 35. C17×M32 | C8 | semidirect |
| 36. #10587483 | C8 | semidirect |
| 37. #10587469 | C8 | semidirect |
| 58. #63216 | C2×C8 | semidirect |
| 59. C16×C17 | C2×C8 | semidirect |
| 60. #63214 | C2×C8 | semidirect |
| 121. M32 | #3633 | semidirect |
| 132. C17 | #11404 | semidirect |
| 154. C16 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #595⋊M32 | 2 |
| C2×#11763893 | 2 |
| #14545804 | 2 |
| #14545803 | 2 |
| M32×#595 | 2 |
| #11404 | 17 |