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. #24909692 | C2 | semidirect |
| 3. #24909514 | C2 | semidirect |
| 5. #24905426 | C2 | semidirect |
| 7. C83×#1364 | C2 | semidirect |
| 132. #1364 | 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 |
| #24909692 | 2 |
| #24909514 | 2 |
| #24906829 | 2 |
| #24905426 | 2 |
| #24905417 | 2 |
| C83×#1364 | 2 |
| #12345 | 83 |