Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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. #24909221 | C2 | semidirect |
| 3. C2×#19127516 | C2 | semidirect |
| 5. #24908376 | C2 | semidirect |
| 7. C83×#1381 | C2 | semidirect |
| 160. #1381 | D83 | semidirect |
| 161. C83 | #13440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581737 | 2 |
| #24909221 | 2 |
| C2×#19127516 | 2 |
| C2×#19127513 | 2 |
| #24908376 | 2 |
| #24908371 | 2 |
| C83×#1381 | 2 |
| #13440 | 83 |