Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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. #14531066 | C2 | semidirect |
| 2. #14531011 | C2 | semidirect |
| 4. #14528378 | C2 | semidirect |
| 6. C16×#3622 | C2 | semidirect |
| 67. C16×C17 | SD16 | semidirect |
| 88. #3622 | SD32 | semidirect |
| 148. C17 | #12505 | semidirect |
| 172. C16 | #63229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531066 | 2 |
| #14531011 | 2 |
| #14531007 | 2 |
| #14528378 | 2 |
| #14528373 | 2 |
| C16×#3622 | 2 |
| C17×#2248 | 2 |
| #12505 | 17 |