Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
272 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 83 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. #24909236 | C2 | semidirect |
| 5. #24905560 | C2 | semidirect |
| 6. #24905556 | C2 | semidirect |
| 7. C83×#1388 | C2 | semidirect |
| 135. #1388 | D83 | semidirect |
| 138. C83 | #13503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909236 | 2 |
| C2×#19127486 | 2 |
| #24907518 | 2 |
| #24907510 | 2 |
| #24905560 | 2 |
| #24905556 | 2 |
| C83×#1388 | 2 |
| #13503 | 83 |