Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
728 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 120 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. C2×#11763827 | C2 | semidirect |
| 2. #14544641 | C2 | semidirect |
| 3. C2×#11763667 | C2 | semidirect |
| 4. #14543662 | C2 | semidirect |
| 62. #10587544 | D4 | semidirect |
| 308. C17 | #9134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763827 | 2 |
| #14544641 | 2 |
| C2×#11763667 | 2 |
| #14543662 | 2 |
| #14537128 | 2 |
| #9134 | 17 |