Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
692 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 105 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×#19128012 | C2 | semidirect |
| 2. #24911935 | C2 | semidirect |
| 3. #24908300 | C2 | semidirect |
| 4. #24907550 | C2 | semidirect |
| 5. #24906031 | C2 | semidirect |
| 6. #24905310 | C2 | semidirect |
| 96. C22⋊Dic83 | D8 | semidirect |
| 234. C83 | #9952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128012 | 2 |
| #24911935 | 2 |
| #24908300 | 2 |
| #24907550 | 2 |
| #24906031 | 2 |
| #24905310 | 2 |
| C83×#3186 | 2 |
| #9952 | 83 |