Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
450 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 127 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. #24907601 | C2 | semidirect |
| 2. #24906148 | C2 | semidirect |
| 3. #24906144 | C2 | semidirect |
| 6. #24905746 | C2 | semidirect |
| 156. C83 | #9769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24907601 | 2 |
| #24906148 | 2 |
| #24906144 | 2 |
| #24906131 | 2 |
| #24905746 | 2 |
| C2×#486×C83 | 2 |
| #9769 | 83 |