Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
586 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 126 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. #14544086 | C2 | semidirect |
| 4. #14543612 | C2 | semidirect |
| 26. C17×#124 | C8 | semidirect |
| 56. C2×Q8×C17 | C2×C8 | semidirect |
| 77. C42×C17 | C2×C8 | semidirect |
| 178. #124 | #3624 | semidirect |
| 204. C17 | #8957 | semidirect |
| 209. C2×Q8 | C2×#3624 | semidirect |
| 242. C42 | C2×#3624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545631 | 2 |
| #14544086 | 2 |
| #14544024 | 2 |
| #14543612 | 2 |
| #124×Dic17 | 2 |
| #8957 | 17 |