Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
358 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 111 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. #24909237 | C2 | semidirect |
| 3. C2×#19127525 | C2 | semidirect |
| 6. #24905569 | C2 | semidirect |
| 7. C83×#1388 | C2 | semidirect |
| 9. #19128119 | C4 | semidirect |
| 143. #1388 | 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 |
| #24909237 | 2 |
| C2×#19127525 | 2 |
| #24907519 | 2 |
| #24907518 | 2 |
| #24905569 | 2 |
| C83×#1388 | 2 |
| #12833 | 83 |