Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
436 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 99 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. C4×#14581727 | C2 | semidirect |
| 3. #24906054 | C2 | semidirect |
| 4. #24905881 | C2 | semidirect |
| 5. #24905880 | C2 | semidirect |
| 6. #24905750 | C2 | semidirect |
| 7. C83×#1525 | C2 | semidirect |
| 187. #1525 | D83 | semidirect |
| 191. C83 | #9726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918038 | 2 |
| C4×#14581727 | 2 |
| #24906054 | 2 |
| #24905881 | 2 |
| #24905880 | 2 |
| #24905750 | 2 |
| C83×#1525 | 2 |
| #9726 | 83 |