Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
500 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 79 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. #24907927 | C2 | semidirect |
| 3. #24907924 | C2 | semidirect |
| 4. #24907648 | C2 | semidirect |
| 5. #24905978 | C2 | semidirect |
| 6. #24905339 | C2 | semidirect |
| 7. C83×#1507 | C2 | semidirect |
| 238. #1507 | D83 | semidirect |
| 240. C83 | #10557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918211 | 2 |
| #24907927 | 2 |
| #24907924 | 2 |
| #24907648 | 2 |
| #24905978 | 2 |
| #24905339 | 2 |
| C83×#1507 | 2 |
| #10557 | 83 |