Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
354 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 6. #11763893 | C4 | semidirect |
| 7. C8×#3633 | C4 | semidirect |
| 28. #10587532 | C8 | semidirect |
| 32. C17×#97 | C8 | semidirect |
| 33. #10587486 | C8 | semidirect |
| 34. #10587486 | C8 | semidirect |
| 35. #10587474 | C8 | semidirect |
| 130. #97 | #3633 | semidirect |
| 137. C17 | #8138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545893 | 2 |
| #14545788 | 2 |
| #14545787 | 2 |
| #14544442 | 2 |
| #8138 | 17 |