Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
578 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 81 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. #24918458 | C2 | semidirect |
| 2. #24917927 | C2 | semidirect |
| 3. #24905931 | C2 | semidirect |
| 4. #24905880 | C2 | semidirect |
| 5. #24905815 | C2 | semidirect |
| 6. #24905334 | C2 | semidirect |
| 7. C83×#3213 | C2 | semidirect |
| 214. #3213 | D83 | semidirect |
| 220. C83 | #10120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918458 | 2 |
| #24917927 | 2 |
| #24905931 | 2 |
| #24905880 | 2 |
| #24905815 | 2 |
| #24905334 | 2 |
| C83×#3213 | 2 |
| #10120 | 83 |