Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
498 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 498 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. #24908383 | C2 | semidirect |
| 3. #24908381 | C2 | semidirect |
| 4. C4×#14581723 | C2 | semidirect |
| 5. #24905959 | C2 | semidirect |
| 6. #24905753 | C2 | semidirect |
| 7. C83×#1502 | C2 | semidirect |
| 9. #19128104 | C4 | semidirect |
| 10. #19128077 | C4 | semidirect |
| 11. #19128049 | C4 | semidirect |
| 12. #19128047 | C4 | semidirect |
| 171. C83⋊C8 | #104 | semidirect |
| 207. #1502 | D83 | semidirect |
| 209. C83 | #9721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918038 | 2 |
| #24908383 | 2 |
| #24908381 | 2 |
| C4×#14581723 | 2 |
| #24905959 | 2 |
| #24905753 | 2 |
| C83×#1502 | 2 |
| #9721 | 83 |