Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
440 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #24905482 | C2 | semidirect |
| 5. #24905481 | C2 | semidirect |
| 6. #24905480 | C2 | semidirect |
| 7. C83×#1350 | C2 | semidirect |
| 184. #1350 | D83 | semidirect |
| 185. C83 | #11712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #467×D83 | 2 |
| #24909072 | 2 |
| #341×D83 | 2 |
| #24905482 | 2 |
| #24905481 | 2 |
| #24905480 | 2 |
| C83×#1350 | 2 |
| #11712 | 83 |