Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
474 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 1. #24918661 | C2 | semidirect |
| 3. #24906014 | C2 | semidirect |
| 4. #24906011 | C2 | semidirect |
| 5. #24906010 | C2 | semidirect |
| 6. C83⋊#1308 | C2 | semidirect |
| 7. C83×#3216 | C2 | semidirect |
| 196. #3216 | D83 | semidirect |
| 202. C83 | #10209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918661 | 2 |
| #24918454 | 2 |
| #24906014 | 2 |
| #24906011 | 2 |
| #24906010 | 2 |
| C83⋊#1308 | 2 |
| C83×#3216 | 2 |
| #10209 | 83 |