Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
458 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 119 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. #24906149 | C2 | semidirect |
| 3. #24906145 | C2 | semidirect |
| 6. #24905755 | C2 | semidirect |
| 7. C83×#1848 | C2 | semidirect |
| 145. #1848 | D83 | semidirect |
| 151. C83 | #9774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128048 | 2 |
| #24906149 | 2 |
| #24906145 | 2 |
| #24906132 | 2 |
| #24905755 | 2 |
| C83×#1848 | 2 |
| #9774 | 83 |