Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
442 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 442 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. #24916539 | C2 | semidirect |
| 2. #24906158 | C2 | semidirect |
| 3. #24906098 | C2 | semidirect |
| 4. #24905862 | C2 | semidirect |
| 5. #24905332 | C2 | semidirect |
| 6. #24905324 | C2 | semidirect |
| 181. C83 | #9371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916539 | 2 |
| #24906158 | 2 |
| #24906098 | 2 |
| #24905862 | 2 |
| #24905332 | 2 |
| #24905324 | 2 |
| C83×#3214 | 2 |
| #9371 | 83 |