Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
616 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 138 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. C4×#10587542 | C2 | semidirect |
| 3. #14543660 | C2 | semidirect |
| 8. #11763664 | C4 | direct (N × H) |
| 40. #10587542 | C2×C4 | semidirect |
| 131. C4×C17 | #329 | semidirect |
| 181. C17 | C4×#329 | semidirect |
| 268. C4 | #11763664 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587542 | 2 |
| C2×#11763664 | 2 |
| #14543660 | 2 |
| C4×#10587622 | 2 |
| C4×#329 | 17 |