Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1450 conjugacy classes of subgroups; only the 299 normal subgroups are shown.
This group has 1450 conjugacy classes of subgroups — too many to draw. Only its 299 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×#11763202 | C2 | semidirect |
| 2. C2×#11763188 | C2 | semidirect |
| 5. #14537180 | C2 | semidirect |
| 7. C4×#10587486 | C2 | semidirect |
| 8. C2×C17×#494 | C2 | semidirect |
| 64. #10587486 | D4 | semidirect |
| 135. C2×#494 | D17 | semidirect |
| 149. C4×C17 | #497 | semidirect |
| 215. C17 | #33305 | semidirect |
| 292. C4 | #11763202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763202 | 2 |
| C2×#11763188 | 2 |
| C2×#11763183 | 2 |
| C2×#11763182 | 2 |
| #14537180 | 2 |
| #14537142 | 2 |
| C4×#10587486 | 2 |
| C2×C17×#494 | 2 |
| #33305 | 17 |