Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
508 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 105 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. #14539729 | C2 | semidirect |
| 3. #14527470 | C2 | semidirect |
| 4. #14527187 | C2 | semidirect |
| 6. #14526679 | C2 | semidirect |
| 83. C2×D4×C17 | Q16 | semidirect |
| 265. C17 | #10182 | semidirect |
| 277. C2×D4 | #63231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539729 | 2 |
| C2×#11763099 | 2 |
| #14527470 | 2 |
| #14527187 | 2 |
| #14527105 | 2 |
| #14526679 | 2 |
| C17×#3077 | 2 |
| #10182 | 17 |