Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1382 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1382 conjugacy classes of subgroups — too many to draw. Only its 331 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 |
|---|---|---|
| 1. C22×#14581711 | C2 | semidirect |
| 2. C2×#19127498 | C2 | direct (N × H) |
| 6. C2×#14581711 | C22 | semidirect |
| 7. #19127498 | C22 | direct (N × H) |
| 19. #14581711 | C23 | semidirect |
| 116. C22×C83 | #355 | semidirect |
| 129. C2×C83 | C2×#355 | semidirect |
| 134. C83 | C22×#355 | semidirect |
| 247. C22 | #19127498 | direct (N × H) |
| 259. C2 | C2×#19127498 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581711 | 2 |
| C2×#19127498 | 2 |
| C22×#124×C83 | 2 |
| C22×#355 | 83 |