Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
398 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #24905573 | C2 | semidirect |
| 5. #24905572 | C2 | semidirect |
| 6. #24905571 | C2 | semidirect |
| 7. C83×#1387 | C2 | semidirect |
| 153. #1387 | D83 | semidirect |
| 154. C83 | #12872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127738 | 2 |
| #24909073 | 2 |
| #24907498 | 2 |
| #24905573 | 2 |
| #24905572 | 2 |
| #24905571 | 2 |
| C83×#1387 | 2 |
| #12872 | 83 |