Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
238 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
| 2. C2×#19127539 | C2 | semidirect |
| 3. C2×#19127538 | C2 | semidirect |
| 5. #24909724 | C2 | semidirect |
| 6. C4×C83⋊C32 | C2 | semidirect |
| 7. C83×#2249 | C2 | semidirect |
| 105. #2249 | D83 | semidirect |
| 107. C83 | #13728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127541 | 2 |
| C2×#19127539 | 2 |
| C2×#19127538 | 2 |
| C2×#19127536 | 2 |
| #24909724 | 2 |
| C4×C83⋊C32 | 2 |
| C83×#2249 | 2 |
| #13728 | 83 |