Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
546 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 81 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. #24914422 | C2 | semidirect |
| 2. #24908694 | C2 | semidirect |
| 3. #24908694 | C2 | semidirect |
| 4. #24905287 | C2 | semidirect |
| 5. #24905285 | C2 | semidirect |
| 6. #24905284 | C2 | semidirect |
| 80. C4⋊Dic83 | D8 | semidirect |
| 238. C83 | #7740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24914422 | 2 |
| #24908694 | 2 |
| #24905287 | 2 |
| #24905285 | 2 |
| #24905284 | 2 |
| C83×#2011 | 2 |
| #7740 | 83 |