Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
290 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 83 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. #24905645 | C2 | semidirect |
| 5. #24905644 | C2 | semidirect |
| 6. #24905643 | C2 | semidirect |
| 7. C83×#1416 | C2 | semidirect |
| 12. Q32×D83 | C4 | semidirect |
| 107. #1416 | D83 | semidirect |
| 108. C83 | #13618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D83 | 2 |
| C2×#19127534 | 2 |
| #24909244 | 2 |
| #24905645 | 2 |
| #24905644 | 2 |
| #24905643 | 2 |
| C83×#1416 | 2 |
| #13618 | 83 |