Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 95 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. #24920597 | C2 | semidirect |
| 2. C2×#19128139 | C2 | semidirect |
| 3. #24917950 | C2 | semidirect |
| 4. #24909178 | C2 | semidirect |
| 5. #24908359 | C2 | semidirect |
| 6. #24905550 | C2 | semidirect |
| 7. C83×#2145 | C2 | semidirect |
| 41. C2×Dic332 | D4 | semidirect |
| 50. C2×D664 | D4 | semidirect |
| 66. C2×C83⋊C16 | D4 | semidirect |
| 82. M32×C83 | D4 | semidirect |
| 221. #2145 | D83 | semidirect |
| 225. C83 | #13334 | semidirect |
| 295. M32 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920597 | 2 |
| C2×#19128139 | 2 |
| #24917950 | 2 |
| #24909178 | 2 |
| #24908359 | 2 |
| #24905550 | 2 |
| C83×#2145 | 2 |
| #13334 | 83 |