Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
528 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. #24908387 | C2 | semidirect |
| 5. #24905962 | C2 | semidirect |
| 6. #24905314 | C2 | semidirect |
| 7. C83×#3165 | C2 | semidirect |
| 108. M16×C83 | SD16 | semidirect |
| 193. #3165 | D83 | semidirect |
| 198. C83 | #10201 | semidirect |
| 289. M16 | #13050577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918775 | 2 |
| #24918591 | 2 |
| #24908387 | 2 |
| #24908382 | 2 |
| #24905962 | 2 |
| #24905314 | 2 |
| C83×#3165 | 2 |
| #10201 | 83 |