Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
402 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 73 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. #24908312 | C2 | semidirect |
| 3. #24906231 | C2 | semidirect |
| 4. #24906186 | C2 | semidirect |
| 5. #24906062 | C2 | semidirect |
| 6. #24906054 | C2 | semidirect |
| 7. C83×#1291 | C2 | semidirect |
| 195. #1291 | D83 | semidirect |
| 196. C83 | #10496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918452 | 2 |
| #24908312 | 2 |
| #24906231 | 2 |
| #24906186 | 2 |
| #24906062 | 2 |
| #24906054 | 2 |
| C83×#1291 | 2 |
| #10496 | 83 |