Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
578 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#19127505 | C2 | semidirect |
| 5. #24908325 | C2 | semidirect |
| 6. #24905540 | C2 | semidirect |
| 7. C22×Q32×C83 | C2 | semidirect |
| 192. C22×Q32 | D83 | semidirect |
| 199. C83 | #13329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581735 | 2 |
| C2×#19128086 | 2 |
| C2×#19127505 | 2 |
| C2×#19127503 | 2 |
| #24908325 | 2 |
| #24905540 | 2 |
| C22×Q32×C83 | 2 |
| #13329 | 83 |