Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
594 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#19128137 | C2 | semidirect |
| 2. #24917906 | C2 | semidirect |
| 3. C2×#19127512 | C2 | semidirect |
| 4. C2×#19127511 | C2 | semidirect |
| 5. #24908340 | C2 | semidirect |
| 6. #24905546 | C2 | semidirect |
| 7. C2×#509×C83 | C2 | semidirect |
| 60. #14581732 | D4 | semidirect |
| 81. C2×D8×C83 | D4 | semidirect |
| 86. M32×C83 | D4 | semidirect |
| 230. C2×#509 | D83 | semidirect |
| 236. C83 | #13341 | semidirect |
| 290. C2×D8 | C22⋊D83 | semidirect |
| 309. M32 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128137 | 2 |
| #24917906 | 2 |
| C2×#19127512 | 2 |
| C2×#19127511 | 2 |
| #24908340 | 2 |
| #24905546 | 2 |
| C2×#509×C83 | 2 |
| #13341 | 83 |