Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
470 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #24916548 | C2 | semidirect |
| 5. #24905360 | C2 | semidirect |
| 6. #24905321 | C2 | semidirect |
| 7. C83×#1805 | C2 | semidirect |
| 11. #19127911 | C4 | semidirect |
| 12. #19127901 | C4 | semidirect |
| 186. #1805 | D83 | semidirect |
| 191. C83 | #9310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916935 | 2 |
| #24916548 | 2 |
| #24906022 | 2 |
| #24905861 | 2 |
| #24905360 | 2 |
| #24905321 | 2 |
| C83×#1805 | 2 |
| #9310 | 83 |