Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #24910211 | C2 | semidirect |
| 3. #24906145 | C2 | semidirect |
| 5. #24905323 | C2 | semidirect |
| 6. #24905292 | C2 | semidirect |
| 9. #19128073 | C4 | semidirect |
| 10. #19128053 | C4 | semidirect |
| 108. C42×C83 | SD16 | semidirect |
| 190. C83 | #9301 | semidirect |
| 291. C42 | #13050578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918385 | 2 |
| #24910211 | 2 |
| #24906145 | 2 |
| #24906023 | 2 |
| #24905323 | 2 |
| #24905292 | 2 |
| C83×#1963 | 2 |
| #9301 | 83 |