Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
412 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 412 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. #24905911 | C2 | semidirect |
| 5. #24905806 | C2 | semidirect |
| 6. C83⋊#1308 | C2 | semidirect |
| 7. C83×#1291 | C2 | semidirect |
| 201. #1291 | D83 | semidirect |
| 202. C83 | #9531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917636 | 2 |
| #24916448 | 2 |
| #24906092 | 2 |
| #24905911 | 2 |
| #24905806 | 2 |
| C83⋊#1308 | 2 |
| C83×#1291 | 2 |
| #9531 | 83 |