Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
2878 conjugacy classes of subgroups; only the 480 normal subgroups are shown.
This group has 2878 conjugacy classes of subgroups — too many to draw. Only its 480 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. C22×C22⋊#3624 | C2 | semidirect |
| 2. C2×#11763652 | C2 | direct (N × H) |
| 6. C2×C22⋊#3624 | C22 | semidirect |
| 7. #11763652 | C22 | direct (N × H) |
| 20. C25×C17 | C8 | semidirect |
| 41. C22⋊#3624 | C23 | semidirect |
| 60. C24×C17 | C2×C8 | semidirect |
| 112. C23×C17 | C22×C8 | semidirect |
| 145. C22×C17 | #323 | semidirect |
| 171. C2×C17 | C2×#323 | semidirect |
| 180. C25 | #3624 | semidirect |
| 202. C17 | C22×#323 | semidirect |
| 219. C24 | C2×#3624 | semidirect |
| 270. C23 | C22×#3624 | semidirect |
| 302. C22 | #11763652 | direct (N × H) |
| 317. C2 | C2×#11763652 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#3624 | 2 |
| C2×#11763652 | 2 |
| C23×C22⋊Dic17 | 2 |
| C22×#323 | 17 |