Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
540 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C2×#19127497 | C2 | semidirect |
| 3. #24907459 | C2 | semidirect |
| 4. C4×#101×C83 | C2 | semidirect |
| 50. #101×C83 | D4 | semidirect |
| 155. C4×C83 | #355 | semidirect |
| 167. C4×#101 | D83 | semidirect |
| 168. C83 | #13226 | semidirect |
| 213. #101 | D332 | semidirect |
| 320. C4 | #19127497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24912462 | 2 |
| C2×#19127497 | 2 |
| #24907459 | 2 |
| C4×#101×C83 | 2 |
| #13226 | 83 |