Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
384 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#19127523 | C2 | semidirect |
| 4. #24908241 | C2 | semidirect |
| 5. #24905575 | C2 | semidirect |
| 6. #24905548 | C2 | semidirect |
| 18. #19127517 | C4 | semidirect |
| 19. #19127514 | C4 | semidirect |
| 152. C83 | #12952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916380 | 2 |
| C2×#19127523 | 2 |
| #24909212 | 2 |
| #24908241 | 2 |
| #24905575 | 2 |
| #24905548 | 2 |
| C2×#360×C83 | 2 |
| #12952 | 83 |