Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
346 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 71 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. #14541132 | C2 | semidirect |
| 2. #14531008 | C2 | semidirect |
| 3. #14530820 | C2 | semidirect |
| 4. #14528139 | C2 | semidirect |
| 5. #14526838 | C2 | semidirect |
| 6. #14526746 | C2 | semidirect |
| 7. C17×D4⋊C16 | C2 | semidirect |
| 93. D4×C17 | D16 | semidirect |
| 126. D4⋊C16 | D17 | semidirect |
| 196. C17 | #12340 | semidirect |
| 246. D4 | D272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14541132 | 2 |
| #14531008 | 2 |
| #14530820 | 2 |
| #14528139 | 2 |
| #14526838 | 2 |
| #14526746 | 2 |
| C17×D4⋊C16 | 2 |
| #12340 | 17 |