Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
222 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 67 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. #24905533 | C2 | semidirect |
| 5. #24905521 | C2 | semidirect |
| 6. #24905518 | C2 | semidirect |
| 7. C83×#1710 | C2 | semidirect |
| 106. #1710 | D83 | semidirect |
| 111. C83 | #12449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909607 | 2 |
| #24909597 | 2 |
| C8×D664 | 2 |
| #24905533 | 2 |
| #24905521 | 2 |
| #24905518 | 2 |
| C83×#1710 | 2 |
| #12449 | 83 |