Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
272 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 85 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. #24909237 | C2 | semidirect |
| 4. #24905576 | C2 | semidirect |
| 5. #24905560 | C2 | semidirect |
| 6. #24905556 | C2 | semidirect |
| 138. C83 | #13503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909237 | 2 |
| C2×#19127485 | 2 |
| #24907517 | 2 |
| #24905576 | 2 |
| #24905560 | 2 |
| #24905556 | 2 |
| C83×#1813 | 2 |
| #13503 | 83 |