Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
422 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 99 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. C4×#14581727 | C2 | semidirect |
| 3. #24906058 | C2 | semidirect |
| 6. #24905744 | C2 | semidirect |
| 7. C83×#1485 | C2 | semidirect |
| 180. #1485 | D83 | semidirect |
| 183. C83 | #9723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918023 | 2 |
| C4×#14581727 | 2 |
| #24906058 | 2 |
| #24906054 | 2 |
| #24905879 | 2 |
| #24905744 | 2 |
| C83×#1485 | 2 |
| #9723 | 83 |