Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
314 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #24919857 | C2 | semidirect |
| 2. #24909686 | C2 | semidirect |
| 4. #24905520 | C2 | semidirect |
| 5. #24905427 | C2 | semidirect |
| 6. #24905417 | C2 | semidirect |
| 7. C83×#2207 | C2 | semidirect |
| 103. D332 | SD32 | semidirect |
| 137. #2207 | D83 | semidirect |
| 142. C83 | #12342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24919857 | 2 |
| #24909686 | 2 |
| #24906815 | 2 |
| #24905520 | 2 |
| #24905427 | 2 |
| #24905417 | 2 |
| C83×#2207 | 2 |
| #12342 | 83 |