Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
544 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 86 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. #14545512 | C2 | semidirect |
| 2. #14544910 | C2 | semidirect |
| 3. #14544282 | C2 | semidirect |
| 4. #14544111 | C2 | semidirect |
| 5. #14543675 | C2 | semidirect |
| 6. #14543623 | C2 | semidirect |
| 134. C2×#3624 | D8 | semidirect |
| 343. C17 | #9049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545512 | 2 |
| #14544910 | 2 |
| #14544282 | 2 |
| #14544111 | 2 |
| #14543675 | 2 |
| #14543623 | 2 |
| #14538781 | 2 |
| #9049 | 17 |