Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
634 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 103 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. #24916923 | C2 | semidirect |
| 2. #24908256 | C2 | semidirect |
| 3. #24905914 | C2 | semidirect |
| 4. #24905338 | C2 | semidirect |
| 5. C83×#3245 | C2 | semidirect |
| 57. C2×D332 | D8 | semidirect |
| 163. #3245 | D83 | semidirect |
| 168. C83 | #10254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916923 | 2 |
| #24908256 | 2 |
| #24905914 | 2 |
| #24905338 | 2 |
| C83×#3245 | 2 |
| #10254 | 83 |