Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
366 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 63 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. #24909597 | C2 | semidirect |
| 3. #24906983 | C2 | semidirect |
| 4. #24905506 | C2 | semidirect |
| 5. #24905431 | C2 | semidirect |
| 6. #24905422 | C2 | semidirect |
| 7. C83×#2243 | C2 | semidirect |
| 18. C4⋊(C83⋊C16) | C22 | semidirect |
| 20. #19127452 | C22 | semidirect |
| 22. #500×C83 | C22 | semidirect |
| 26. #346×C83 | C22 | semidirect |
| 166. #2243 | D83 | semidirect |
| 172. C83 | #12376 | semidirect |
| 175. #500 | C2×D83 | semidirect |
| 189. #346 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24919072 | 2 |
| #24909597 | 2 |
| #24906983 | 2 |
| #24905506 | 2 |
| #24905431 | 2 |
| #24905422 | 2 |
| C83×#2243 | 2 |
| #12376 | 83 |