Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
542 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 542 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 |
|---|---|---|
| 4. #24906065 | C2 | semidirect |
| 5. #24905975 | C2 | semidirect |
| 6. #24905355 | C2 | semidirect |
| 7. C83×#3236 | C2 | semidirect |
| 179. #3236 | D83 | semidirect |
| 186. C83 | #10097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917839 | 2 |
| #24913409 | 2 |
| #24906176 | 2 |
| #24906065 | 2 |
| #24905975 | 2 |
| #24905355 | 2 |
| C83×#3236 | 2 |
| #10097 | 83 |