Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
332 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 107 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. #24906226 | C2 | semidirect |
| 3. #24905428 | C2 | semidirect |
| 4. #24905425 | C2 | semidirect |
| 5. C2×C4×C16×C83 | C2 | semidirect |
| 139. C2×C4×C16 | D83 | semidirect |
| 143. C83 | #11673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918033 | 2 |
| #24906226 | 2 |
| #24905428 | 2 |
| #24905425 | 2 |
| C2×C4×C16×C83 | 2 |
| #11673 | 83 |