Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
224 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 71 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. #14545843 | C2 | semidirect |
| 4. Q8⋊#63241 | C2 | semidirect |
| 6. C8×#63241 | C2 | semidirect |
| 58. #63241 | SD16 | semidirect |
| 89. #3622 | M32 | semidirect |
| 149. C17 | #12051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14546010 | 2 |
| #14545999 | 2 |
| #14545843 | 2 |
| Q8⋊#63241 | 2 |
| #14545827 | 2 |
| C8×#63241 | 2 |
| #14544368 | 2 |
| #12051 | 17 |