Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
396 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 396 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. #24906078 | C2 | semidirect |
| 5. #24905324 | C2 | semidirect |
| 6. #24905293 | C2 | semidirect |
| 7. C83×#2985 | C2 | semidirect |
| 164. #2985 | D83 | semidirect |
| 170. C83 | #9284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918599 | 2 |
| #24906078 | 2 |
| #24906075 | 2 |
| #24905933 | 2 |
| #24905324 | 2 |
| #24905293 | 2 |
| C83×#2985 | 2 |
| #9284 | 83 |