Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
462 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 108 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. #14544985 | C2 | semidirect |
| 2. #14544326 | C2 | semidirect |
| 3. #14543743 | C2 | semidirect |
| 4. #14543742 | C2 | semidirect |
| 8. #11763698 | C22 | semidirect |
| 11. #11763670 | C22 | semidirect |
| 32. D8×D17 | C8 | semidirect |
| 75. D8×C17 | C2×C8 | semidirect |
| 93. D136 | C2×C8 | semidirect |
| 180. D17 | #1333 | semidirect |
| 215. C17 | C2×#1333 | semidirect |
| 235. D8 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544985 | 2 |
| #14544326 | 2 |
| #14543743 | 2 |
| #14543742 | 2 |
| C4×D8×D17 | 2 |
| C2×#1333 | 17 |