Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
348 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 75 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. #24908456 | C2 | semidirect |
| 3. #24906230 | C2 | semidirect |
| 5. #24906064 | C2 | semidirect |
| 6. #24905335 | C2 | semidirect |
| 173. C83 | #10497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918649 | 2 |
| #24908456 | 2 |
| #24906230 | 2 |
| #24906185 | 2 |
| #24906064 | 2 |
| #24905335 | 2 |
| C83×#1525 | 2 |
| #10497 | 83 |