Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
456 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #24908306 | C2 | semidirect |
| 4. #24906149 | C2 | semidirect |
| 6. #24905352 | C2 | semidirect |
| 7. C83×#1309 | C2 | semidirect |
| 141. D332 | #101 | semidirect |
| 189. #1309 | D83 | semidirect |
| 191. C83 | #9357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917279 | 2 |
| #24916589 | 2 |
| #24908306 | 2 |
| #24906149 | 2 |
| #24905900 | 2 |
| #24905352 | 2 |
| C83×#1309 | 2 |
| #9357 | 83 |