Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
424 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 69 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. #24909117 | C2 | semidirect |
| 5. #24907749 | C2 | semidirect |
| 6. #24905591 | C2 | semidirect |
| 7. C83×#1909 | C2 | semidirect |
| 199. #1909 | D83 | semidirect |
| 202. C83 | #13434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918330 | 2 |
| #24909134 | 2 |
| #24909117 | 2 |
| #24908010 | 2 |
| #24907749 | 2 |
| #24905591 | 2 |
| C83×#1909 | 2 |
| #13434 | 83 |