Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
540 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 102 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. #14545703 | C2 | semidirect |
| 2. #14544905 | C2 | semidirect |
| 3. #14544083 | C2 | semidirect |
| 4. #14544075 | C2 | semidirect |
| 5. #14543630 | C2 | semidirect |
| 6. #14543617 | C2 | semidirect |
| 97. C2×D4×C17 | M16 | semidirect |
| 121. M16×C17 | M16 | semidirect |
| 311. C17 | #8956 | semidirect |
| 324. C2×D4 | #63247 | semidirect |
| 343. M16 | #63247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545703 | 2 |
| #14544905 | 2 |
| #14544083 | 2 |
| #14544075 | 2 |
| #14543630 | 2 |
| #14543617 | 2 |
| AGL(1,ℤ/8)×Dic17 | 2 |
| #8956 | 17 |