Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
562 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#19128020 | C2 | semidirect |
| 3. C2×#19128015 | C2 | semidirect |
| 4. #24907541 | C2 | semidirect |
| 5. #24905822 | C2 | semidirect |
| 6. #24905822 | C2 | semidirect |
| 7. C83×#1298 | C2 | semidirect |
| 209. #1298 | D83 | semidirect |
| 210. C83 | #9992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918263 | 2 |
| C2×#19128020 | 2 |
| C2×#19128015 | 2 |
| #24907541 | 2 |
| #24905822 | 2 |
| C83×#1298 | 2 |
| #9992 | 83 |