Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
494 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 232 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. #14545200 | C2 | semidirect |
| 2. Q8×#63216 | C2 | semidirect |
| 127. C17 | #33498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545200 | 2 |
| Q8×#63216 | 2 |
| #14545148 | 2 |
| #14545143 | 2 |
| C8×Q8×D17 | 2 |
| #33498 | 17 |