Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
586 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 3. C2×#11763654 | C2 | semidirect |
| 4. #14543627 | C2 | semidirect |
| 34. C17×#123 | C8 | semidirect |
| 76. C22×C4×C17 | C2×C8 | semidirect |
| 99. C22⋊C4×C17 | C2×C8 | semidirect |
| 228. #123 | #3624 | semidirect |
| 258. C17 | #9108 | semidirect |
| 284. C22×C4 | C2×#3624 | semidirect |
| 303. C22⋊C4 | C2×#3624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545631 | 2 |
| #14544020 | 2 |
| C2×#11763654 | 2 |
| #14543627 | 2 |
| #14531456 | 2 |
| #9108 | 17 |