Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
490 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 81 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. #24907927 | C2 | semidirect |
| 2. #24907902 | C2 | semidirect |
| 3. #24907667 | C2 | semidirect |
| 4. #24906031 | C2 | semidirect |
| 5. #24905823 | C2 | semidirect |
| 6. #24905368 | C2 | semidirect |
| 232. C83 | #10560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24907927 | 2 |
| #24907902 | 2 |
| #24907667 | 2 |
| #24906031 | 2 |
| #24905823 | 2 |
| #24905368 | 2 |
| C83×#3192 | 2 |
| #10560 | 83 |