Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
554 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24918846 | C2 | semidirect |
| 3. #24908441 | C2 | semidirect |
| 4. #24908292 | C2 | semidirect |
| 5. #24908290 | C2 | semidirect |
| 6. C83⋊#1309 | C2 | semidirect |
| 7. C83×#3254 | C2 | semidirect |
| 220. #3254 | D83 | semidirect |
| 226. C83 | #10301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918846 | 2 |
| #24918841 | 2 |
| #24908441 | 2 |
| #24908292 | 2 |
| #24908290 | 2 |
| C83⋊#1309 | 2 |
| C83×#3254 | 2 |
| #10301 | 83 |