Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
430 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 93 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×#19127517 | C2 | semidirect |
| 5. #24908246 | C2 | semidirect |
| 6. #24905551 | C2 | semidirect |
| 7. C2×#358×C83 | C2 | semidirect |
| 185. C2×#358 | D83 | semidirect |
| 188. C83 | #13412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917952 | 2 |
| C2×#19127517 | 2 |
| C2×#19127509 | 2 |
| #24909173 | 2 |
| #24908246 | 2 |
| #24905551 | 2 |
| C2×#358×C83 | 2 |
| #13412 | 83 |