Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
780 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. #24911107 | C2 | semidirect |
| 4. #24907386 | C2 | semidirect |
| 5. #24905984 | C2 | semidirect |
| 6. #24905349 | C2 | semidirect |
| 231. C83 | #10330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918269 | 2 |
| #24911122 | 2 |
| #24911107 | 2 |
| #24907386 | 2 |
| #24905984 | 2 |
| #24905349 | 2 |
| C83×#1507 | 2 |
| #10330 | 83 |