Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
324 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 4. #24907345 | C2 | semidirect |
| 5. #24905560 | C2 | semidirect |
| 6. #24905540 | C2 | semidirect |
| 7. C2×#368×C83 | C2 | semidirect |
| 16. #19127506 | C4 | semidirect |
| 17. #19127506 | C4 | semidirect |
| 18. #19127503 | C4 | semidirect |
| 19. #19127503 | C4 | semidirect |
| 154. C2×#368 | D83 | semidirect |
| 161. C83 | #13134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127507 | 2 |
| #24909171 | 2 |
| #24908349 | 2 |
| #24907345 | 2 |
| #24905560 | 2 |
| #24905540 | 2 |
| C2×#368×C83 | 2 |
| #13134 | 83 |