Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
574 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 101 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. #24918584 | C2 | semidirect |
| 3. #24908284 | C2 | semidirect |
| 4. #24906024 | C2 | semidirect |
| 5. #24906023 | C2 | semidirect |
| 6. #24905307 | C2 | semidirect |
| 7. C83×#3226 | C2 | semidirect |
| 199. #3226 | D83 | semidirect |
| 205. C83 | #10225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918584 | 2 |
| #24917908 | 2 |
| #24908284 | 2 |
| #24906024 | 2 |
| #24906023 | 2 |
| #24905307 | 2 |
| C83×#3226 | 2 |
| #10225 | 83 |