Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#19127968 | C2 | semidirect |
| 3. #24917135 | C2 | semidirect |
| 4. C2×#19127509 | C2 | semidirect |
| 5. C2×#19127484 | C2 | semidirect |
| 6. #24905571 | C2 | semidirect |
| 7. C2×#357×C83 | C2 | semidirect |
| 60. #14581732 | D4 | semidirect |
| 63. #14581728 | D4 | semidirect |
| 73. C2×D8×C83 | D4 | semidirect |
| 223. C2×#357 | D83 | semidirect |
| 226. C83 | #13307 | semidirect |
| 269. C2×D8 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128137 | 2 |
| C2×#19127968 | 2 |
| #24917135 | 2 |
| C2×#19127509 | 2 |
| C2×#19127484 | 2 |
| #24905571 | 2 |
| C2×#357×C83 | 2 |
| #13307 | 83 |