Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
228 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 58 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. #14543826 | C2 | semidirect |
| 2. #14543624 | C2 | semidirect |
| 14. C2×Q16×C17 | C8 | semidirect |
| 16. C2×D8×C17 | C8 | semidirect |
| 120. C2×Q16 | #3624 | semidirect |
| 122. C2×D8 | #3624 | semidirect |
| 139. C17 | #7109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14543826 | 2 |
| #14543624 | 2 |
| #14529678 | 2 |
| #7109 | 17 |