Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
936 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×#19128451 | C2 | semidirect |
| 2. #24918649 | C2 | semidirect |
| 3. #24906772 | C2 | semidirect |
| 4. #24906759 | C2 | semidirect |
| 5. #24906087 | C2 | semidirect |
| 6. #24906064 | C2 | semidirect |
| 16. #19128107 | C22 | semidirect |
| 17. #19128065 | C22 | semidirect |
| 22. #19127442 | C22 | semidirect |
| 194. C83 | #18994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128451 | 2 |
| #24918649 | 2 |
| #24906772 | 2 |
| #24906759 | 2 |
| #24906087 | 2 |
| #24906064 | 2 |
| C83×#3153 | 2 |
| #18994 | 83 |