Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
282 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×#63216 | C8 | semidirect |
| 33. #10587529 | C8 | semidirect |
| 36. C2×C16×C17 | C8 | semidirect |
| 37. C2×#63214 | C8 | semidirect |
| 38. C16×D17 | C8 | semidirect |
| 39. C16×D17 | C8 | semidirect |
| 130. C2×C16 | #3633 | semidirect |
| 138. C17 | #11405 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #595⋊M32 | 2 |
| #14545893 | 2 |
| #14545804 | 2 |
| #14545803 | 2 |
| C2×#11763696 | 2 |
| #11405 | 17 |