Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 103 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. #24916558 | C2 | semidirect |
| 2. #24906163 | C2 | semidirect |
| 5. #24905332 | C2 | semidirect |
| 6. #24905324 | C2 | semidirect |
| 167. C83 | #9372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916558 | 2 |
| #24906163 | 2 |
| #24906098 | 2 |
| #24905862 | 2 |
| #24905332 | 2 |
| #24905324 | 2 |
| C83×#3235 | 2 |
| #9372 | 83 |