Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
478 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 80 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. #14545475 | C2 | semidirect |
| 2. #14544691 | C2 | semidirect |
| 5. #14543656 | C2 | semidirect |
| 6. #14543626 | C2 | semidirect |
| 28. C2×#10587479 | C4 | semidirect |
| 29. C2×#10587492 | C4 | semidirect |
| 30. C2×#10587480 | C4 | semidirect |
| 32. C2×C17×#107 | C4 | semidirect |
| 232. C2×#107 | #595 | semidirect |
| 304. C17 | #9242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545475 | 2 |
| #14544691 | 2 |
| #14544181 | 2 |
| #14544061 | 2 |
| #14543656 | 2 |
| #14543626 | 2 |
| C2×#11763136 | 2 |
| #9242 | 17 |