Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
606 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 86 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. #14544974 | C2 | semidirect |
| 4. C2×#11763662 | C2 | semidirect |
| 5. #14543659 | C2 | semidirect |
| 6. #14543625 | C2 | semidirect |
| 27. #11763127 | C4 | semidirect |
| 31. #11762950 | C4 | semidirect |
| 32. #11762947 | C4 | semidirect |
| 34. C17×#481 | C4 | semidirect |
| 40. C22×Dic34 | C2×C4 | semidirect |
| 55. C2×C4⋊C4×C17 | C2×C4 | semidirect |
| 83. C17×C22⋊C8 | C2×C4 | semidirect |
| 84. C22⋊#3622 | C2×C4 | semidirect |
| 137. C22⋊#595 | SD16 | semidirect |
| 285. #481 | #595 | semidirect |
| 344. C2×C4⋊C4 | C2×#595 | semidirect |
| 365. C22⋊C8 | C2×#595 | semidirect |
| 373. C17 | #9275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545312 | 2 |
| #14544974 | 2 |
| #14544219 | 2 |
| C2×#11763662 | 2 |
| #14543659 | 2 |
| #14543625 | 2 |
| #14539543 | 2 |
| #9275 | 17 |