Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1502 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 320 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×#10587542 | C2 | semidirect |
| 2. C2×#11763665 | C2 | direct (N × H) |
| 6. C2×#10587542 | C22 | semidirect |
| 7. #11763665 | C22 | direct (N × H) |
| 37. #10587542 | C23 | semidirect |
| 92. C22×C17 | #329 | semidirect |
| 115. C2×C17 | C2×#329 | semidirect |
| 142. C17 | C22×#329 | semidirect |
| 196. C22 | #11763665 | direct (N × H) |
| 206. C2 | C2×#11763665 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587542 | 2 |
| C2×#11763665 | 2 |
| C22×#10587633 | 2 |
| C22×#329 | 17 |