Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
690 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 111 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. #24918388 | C2 | semidirect |
| 3. C2×#19128075 | C2 | semidirect |
| 4. #24906132 | C2 | semidirect |
| 5. #24905913 | C2 | semidirect |
| 6. #24905301 | C2 | semidirect |
| 7. C83×#1997 | C2 | semidirect |
| 111. M16×C83 | SD16 | semidirect |
| 191. #1997 | D83 | semidirect |
| 195. C83 | #10146 | semidirect |
| 292. M16 | #13050577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918388 | 2 |
| #24917915 | 2 |
| C2×#19128075 | 2 |
| #24906132 | 2 |
| #24905913 | 2 |
| #24905301 | 2 |
| C83×#1997 | 2 |
| #10146 | 83 |