Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
534 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 85 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. #24917859 | C2 | semidirect |
| 3. #24906180 | C2 | semidirect |
| 4. #24906061 | C2 | semidirect |
| 5. #24905970 | C2 | semidirect |
| 6. #24905356 | C2 | semidirect |
| 7. C83×#2640 | C2 | semidirect |
| 190. #2640 | D83 | semidirect |
| 195. C83 | #10092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918450 | 2 |
| #24917859 | 2 |
| #24906180 | 2 |
| #24906061 | 2 |
| #24905970 | 2 |
| #24905356 | 2 |
| C83×#2640 | 2 |
| #10092 | 83 |