Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
556 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24918846 | C2 | semidirect |
| 3. #24908304 | C2 | semidirect |
| 4. #24906054 | C2 | semidirect |
| 5. #24905884 | C2 | semidirect |
| 6. #24905353 | C2 | semidirect |
| 7. C83×#3138 | C2 | semidirect |
| 195. #3138 | D83 | semidirect |
| 200. C83 | #10112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918846 | 2 |
| #24918381 | 2 |
| #24908304 | 2 |
| #24906054 | 2 |
| #24905884 | 2 |
| #24905353 | 2 |
| C83×#3138 | 2 |
| #10112 | 83 |