Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
180 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#19127541 | C2 | semidirect |
| 4. #24905666 | C2 | semidirect |
| 5. #24905656 | C2 | semidirect |
| 6. #24905655 | C2 | semidirect |
| 97. C83 | #13701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127541 | 2 |
| #24909757 | 2 |
| #24909588 | 2 |
| #24905666 | 2 |
| #24905656 | 2 |
| #24905655 | 2 |
| C83×#2222 | 2 |
| #13701 | 83 |