Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
306 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #24909068 | C2 | semidirect |
| 5. #24905577 | C2 | semidirect |
| 6. #24905570 | C2 | semidirect |
| 7. C83×#1951 | C2 | semidirect |
| 14. #19127516 | C4 | semidirect |
| 15. #19127513 | C4 | semidirect |
| 144. #1951 | D83 | semidirect |
| 147. C83 | #13156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909210 | 2 |
| C2×#19127510 | 2 |
| #24909068 | 2 |
| #24908361 | 2 |
| #24905577 | 2 |
| #24905570 | 2 |
| C83×#1951 | 2 |
| #13156 | 83 |