Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×#19127524 | C2 | semidirect |
| 5. #24905574 | C2 | semidirect |
| 6. #24905568 | C2 | semidirect |
| 7. C83×#2155 | C2 | semidirect |
| 10. #19128117 | C4 | semidirect |
| 139. #2155 | D83 | semidirect |
| 145. C83 | #12833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920565 | 2 |
| C2×#19127524 | 2 |
| #24907519 | 2 |
| #24907514 | 2 |
| #24905574 | 2 |
| #24905568 | 2 |
| C83×#2155 | 2 |
| #12833 | 83 |