Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
626 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. #24915861 | C2 | semidirect |
| 4. #24906149 | C2 | semidirect |
| 5. #24906145 | C2 | semidirect |
| 6. #24905296 | C2 | semidirect |
| 112. C42×C83 | SD16 | semidirect |
| 182. C83 | #10283 | semidirect |
| 287. C42 | #13050578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918588 | 2 |
| #24918385 | 2 |
| #24915861 | 2 |
| #24906149 | 2 |
| #24906145 | 2 |
| #24905296 | 2 |
| C83×#1962 | 2 |
| #10283 | 83 |