Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
602 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 131 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. #24908303 | C2 | semidirect |
| 3. #24906219 | C2 | semidirect |
| 4. #24906130 | C2 | semidirect |
| 5. C83×#1451 | C2 | semidirect |
| 97. C8×C83 | #100 | semidirect |
| 123. #1451 | D83 | semidirect |
| 124. C83 | #9811 | semidirect |
| 217. C8 | #14581708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128078 | 2 |
| #24908303 | 2 |
| #24906219 | 2 |
| #24906130 | 2 |
| C83×#1451 | 2 |
| #9811 | 83 |