Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
244 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 71 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. #24906823 | C2 | semidirect |
| 3. #24905537 | C2 | semidirect |
| 4. #24905510 | C2 | semidirect |
| 5. C83×#2183 | C2 | semidirect |
| 51. C16×C83 | SD16 | semidirect |
| 85. #2183 | D83 | semidirect |
| 89. C83 | #12442 | semidirect |
| 135. C16 | #13050577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909713 | 2 |
| #24906823 | 2 |
| #24905537 | 2 |
| #24905510 | 2 |
| C83×#2183 | 2 |
| #12442 | 83 |