Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
626 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 113 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. #24916486 | C2 | semidirect |
| 3. #24907452 | C2 | semidirect |
| 4. #24905889 | C2 | semidirect |
| 5. #24905887 | C2 | semidirect |
| 6. #24905321 | C2 | semidirect |
| 7. C83×#1286 | C2 | semidirect |
| 56. C4×C83⋊C8 | D4 | semidirect |
| 65. C4×C8×C83 | D4 | semidirect |
| 216. #1286 | D83 | semidirect |
| 217. C83 | #9485 | semidirect |
| 274. C4×C8 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916486 | 2 |
| #24912365 | 2 |
| #24907452 | 2 |
| #24905889 | 2 |
| #24905887 | 2 |
| #24905321 | 2 |
| C83×#1286 | 2 |
| #9485 | 83 |