Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
540 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24916533 | C2 | semidirect |
| 3. #24906176 | C2 | semidirect |
| 4. #24906176 | C2 | semidirect |
| 5. #24906097 | C2 | semidirect |
| 6. #24905335 | C2 | semidirect |
| 7. C83×#1291 | C2 | semidirect |
| 170. #1291 | D83 | semidirect |
| 171. C83 | #9423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917915 | 2 |
| #24916533 | 2 |
| #24906176 | 2 |
| #24906097 | 2 |
| #24905335 | 2 |
| C83×#1291 | 2 |
| #9423 | 83 |