Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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. #14546010 | C2 | semidirect |
| 3. #14545849 | C2 | semidirect |
| 4. Q8⋊#63241 | C2 | semidirect |
| 6. #14545801 | C2 | semidirect |
| 89. #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 |
|---|---|
| #14546010 | 2 |
| #14545999 | 2 |
| #14545849 | 2 |
| Q8⋊#63241 | 2 |
| #14545827 | 2 |
| #14545801 | 2 |
| #14544368 | 2 |
| #12058 | 17 |