Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
542 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 99 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. #24917985 | C2 | semidirect |
| 5. #24906026 | C2 | semidirect |
| 6. #24905307 | C2 | semidirect |
| 7. C83×#1518 | C2 | semidirect |
| 94. C2×C83⋊C8 | SD16 | semidirect |
| 192. #1518 | D83 | semidirect |
| 194. C83 | #10220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918406 | 2 |
| #24918401 | 2 |
| #24917985 | 2 |
| #24908286 | 2 |
| #24906026 | 2 |
| #24905307 | 2 |
| C83×#1518 | 2 |
| #10220 | 83 |