Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 2. #24909266 | C2 | semidirect |
| 3. #24905474 | C2 | semidirect |
| 5. C83×#1834 | C2 | semidirect |
| 7. #19128103 | C4 | semidirect |
| 8. #19128085 | C4 | semidirect |
| 13. C4×Dic332 | C4 | semidirect |
| 15. C4×D664 | C4 | semidirect |
| 150. #1834 | D83 | semidirect |
| 153. C83 | #11860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918033 | 2 |
| #24909266 | 2 |
| #24905474 | 2 |
| #24905471 | 2 |
| C83×#1834 | 2 |
| #11860 | 83 |