Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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. #24908439 | C2 | semidirect |
| 4. C4×#14581702 | C2 | semidirect |
| 5. #24905917 | C2 | semidirect |
| 7. C83×#1567 | C2 | semidirect |
| 10. #19128099 | C4 | semidirect |
| 11. #19128074 | C4 | semidirect |
| 12. #19128052 | C4 | semidirect |
| 13. #19128048 | C4 | semidirect |
| 140. C8×C83 | #104 | semidirect |
| 170. #1567 | D83 | semidirect |
| 173. C83 | #9851 | semidirect |
| 307. C8 | #14581718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918022 | 2 |
| #24908439 | 2 |
| #24908290 | 2 |
| C4×#14581702 | 2 |
| #24905917 | 2 |
| #24905913 | 2 |
| C83×#1567 | 2 |
| #9851 | 83 |