Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
656 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 227 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. #24908027 | C2 | semidirect |
| 4. #24907608 | C2 | semidirect |
| 5. #24907337 | C2 | semidirect |
| 7. C83×#1726 | C2 | semidirect |
| 123. #1726 | D83 | semidirect |
| 124. C83 | #21670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24910761 | 2 |
| #24908076 | 2 |
| #24908027 | 2 |
| #24907608 | 2 |
| #24907337 | 2 |
| #24907246 | 2 |
| C83×#1726 | 2 |
| #21670 | 83 |