Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1262 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1262 conjugacy classes of subgroups — too many to draw. Only its 309 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×#10587670 | C2 | semidirect |
| 2. C2×#11763908 | C2 | direct (N × H) |
| 5. C2×#10587670 | C22 | semidirect |
| 7. #11763908 | C22 | direct (N × H) |
| 38. #10587670 | C23 | semidirect |
| 110. C22×C17 | #349 | semidirect |
| 136. C2×C17 | C2×#349 | semidirect |
| 164. C17 | C22×#349 | semidirect |
| 235. C22 | #11763908 | direct (N × H) |
| 247. C2 | C2×#11763908 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587670 | 2 |
| C2×#11763908 | 2 |
| C23×#63243 | 2 |
| C22×#349 | 17 |