Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
290 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 65 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. #24909510 | C2 | semidirect |
| 4. #24905518 | C2 | semidirect |
| 5. #24905428 | C2 | semidirect |
| 7. C83×#2241 | C2 | semidirect |
| 129. #2241 | D83 | semidirect |
| 135. C83 | #12345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24919893 | 2 |
| #24909510 | 2 |
| #24906825 | 2 |
| #24905518 | 2 |
| #24905428 | 2 |
| #24905419 | 2 |
| C83×#2241 | 2 |
| #12345 | 83 |