Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
558 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 558 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. #24916180 | C2 | semidirect |
| 3. #24908288 | C2 | semidirect |
| 4. #24906024 | C2 | semidirect |
| 5. #24905323 | C2 | semidirect |
| 6. #24905293 | C2 | semidirect |
| 7. C83×#1545 | C2 | semidirect |
| 10. #19128077 | C4 | semidirect |
| 11. #19128047 | C4 | semidirect |
| 87. C2×C83⋊C8 | D8 | semidirect |
| 199. #1545 | D83 | semidirect |
| 203. C83 | #9293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918381 | 2 |
| #24916180 | 2 |
| #24908288 | 2 |
| #24906024 | 2 |
| #24905323 | 2 |
| #24905293 | 2 |
| C83×#1545 | 2 |
| #9293 | 83 |