Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
722 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 722 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 |
|---|---|---|
| 1. #14545631 | C2 | semidirect |
| 2. #14544083 | C2 | semidirect |
| 3. #14544024 | C2 | semidirect |
| 4. #14543612 | C2 | semidirect |
| 28. C17×#127 | C8 | semidirect |
| 50. C4⋊#3624 | D4 | semidirect |
| 64. C2×D4×C17 | C2×C8 | semidirect |
| 83. C42×C17 | C2×C8 | semidirect |
| 196. #127 | #3624 | semidirect |
| 221. C17 | #8959 | semidirect |
| 233. C2×D4 | C2×#3624 | semidirect |
| 264. 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 |
| #14544083 | 2 |
| #14544024 | 2 |
| #14543612 | 2 |
| #127×Dic17 | 2 |
| #8959 | 17 |