Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
468 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 1. #24918854 | C2 | semidirect |
| 5. #24905974 | C2 | semidirect |
| 6. #24905373 | C2 | semidirect |
| 7. C83×#1506 | C2 | semidirect |
| 197. #1506 | D83 | semidirect |
| 199. C83 | #10216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918854 | 2 |
| #24918663 | 2 |
| #24918661 | 2 |
| #24908295 | 2 |
| #24905974 | 2 |
| #24905373 | 2 |
| C83×#1506 | 2 |
| #10216 | 83 |