Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
392 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 392 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. #24909213 | C2 | semidirect |
| 3. #24908351 | C2 | semidirect |
| 4. #24905567 | C2 | semidirect |
| 5. C83×#2150 | C2 | semidirect |
| 115. #2150 | D83 | semidirect |
| 119. C83 | #13444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920599 | 2 |
| #24909213 | 2 |
| #24908351 | 2 |
| #24905567 | 2 |
| C83×#2150 | 2 |
| #13444 | 83 |