Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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. #24909236 | C2 | semidirect |
| 5. #24905560 | C2 | semidirect |
| 6. #24905558 | C2 | semidirect |
| 7. C83×#2155 | C2 | semidirect |
| 11. C2×#14581731 | C4 | semidirect |
| 13. C2×C16×D83 | C4 | semidirect |
| 142. #2155 | D83 | semidirect |
| 147. C83 | #12832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128119 | 2 |
| #24909236 | 2 |
| #24907510 | 2 |
| #24907506 | 2 |
| #24905560 | 2 |
| #24905558 | 2 |
| C83×#2155 | 2 |
| #12832 | 83 |