Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
414 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #24906065 | C2 | semidirect |
| 5. #24905373 | C2 | semidirect |
| 6. #24905354 | C2 | semidirect |
| 7. C83×#1470 | C2 | semidirect |
| 190. #1470 | D83 | semidirect |
| 193. C83 | #9352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917281 | 2 |
| #24916480 | 2 |
| #24906065 | 2 |
| #24905898 | 2 |
| #24905373 | 2 |
| #24905354 | 2 |
| C83×#1470 | 2 |
| #9352 | 83 |