Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
434 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#19127516 | C2 | semidirect |
| 5. #24909182 | C2 | semidirect |
| 6. #24909068 | C2 | semidirect |
| 7. C83×#1833 | C2 | semidirect |
| 15. #19128085 | C4 | semidirect |
| 16. #19128081 | C4 | semidirect |
| 175. #1833 | D83 | semidirect |
| 176. C83 | #13216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917957 | 2 |
| C2×#19127516 | 2 |
| #24909198 | 2 |
| #24909190 | 2 |
| #24909182 | 2 |
| #24909068 | 2 |
| C83×#1833 | 2 |
| #13216 | 83 |