Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
300 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 300 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 |
|---|---|---|
| 1. #24909221 | C2 | semidirect |
| 3. #24909067 | C2 | semidirect |
| 5. #24905551 | C2 | semidirect |
| 6. #24905550 | C2 | semidirect |
| 145. C83 | #13126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909221 | 2 |
| #24909091 | 2 |
| #24909067 | 2 |
| #24907263 | 2 |
| #24905551 | 2 |
| #24905550 | 2 |
| C2×#350×C83 | 2 |
| #13126 | 83 |