Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
218 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 76 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. #14545199 | C2 | semidirect |
| 3. #14543814 | C2 | semidirect |
| 4. Q8⋊#63216 | C2 | semidirect |
| 6. #14543699 | C2 | semidirect |
| 87. #3622 | M32 | semidirect |
| 149. C17 | #12058 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545199 | 2 |
| #14545170 | 2 |
| #14543814 | 2 |
| Q8⋊#63216 | 2 |
| #14543735 | 2 |
| #14543699 | 2 |
| #14527581 | 2 |
| #12058 | 17 |