Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
310 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 83 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. #24907582 | C2 | semidirect |
| 5. #24905358 | C2 | semidirect |
| 6. #24905291 | C2 | semidirect |
| 7. C83×#1301 | C2 | semidirect |
| 158. #1301 | D83 | semidirect |
| 160. C83 | #10629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24908294 | 2 |
| #24907582 | 2 |
| #24906113 | 2 |
| #24906110 | 2 |
| #24905358 | 2 |
| #24905291 | 2 |
| C83×#1301 | 2 |
| #10629 | 83 |