Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
6046 conjugacy classes of subgroups; only the 1539 normal subgroups are shown.
This group has 6046 conjugacy classes of subgroups — too many to draw. Only its 1539 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 |
|---|---|---|
| 2. C2×#11762728 | C2 | direct (N × H) |
| 9. #11762728 | C22 | direct (N × H) |
| 24. C23×Dic17 | Q8 | semidirect |
| 45. C22×Dic17 | C2×Q8 | semidirect |
| 66. C2×Dic17 | C22×Q8 | semidirect |
| 71. C22×C17 | #395 | semidirect |
| 90. C2×C17 | C2×#395 | semidirect |
| 110. C17 | C22×#395 | semidirect |
| 147. C22 | #11762728 | direct (N × H) |
| 157. C2 | C2×#11762728 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#63225 | 2 |
| C2×#11762728 | 2 |
| C22×#10587502 | 2 |
| C24×Q8×C17 | 2 |
| C22×#395 | 17 |