Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
488 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 2. #14544953 | C2 | semidirect |
| 3. #14544086 | C2 | semidirect |
| 5. #14543630 | C2 | semidirect |
| 6. #14543617 | C2 | semidirect |
| 88. C2×Q8×C17 | M16 | semidirect |
| 139. #63223 | M16 | semidirect |
| 297. C17 | #8955 | semidirect |
| 308. C2×Q8 | #63243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545705 | 2 |
| #14544953 | 2 |
| #14544086 | 2 |
| #14544077 | 2 |
| #14543630 | 2 |
| #14543617 | 2 |
| #14537599 | 2 |
| #8955 | 17 |