Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
528 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #24908400 | C2 | semidirect |
| 4. #24905918 | C2 | semidirect |
| 6. #24905337 | C2 | semidirect |
| 7. C83×#3078 | C2 | semidirect |
| 116. C2×Q8×C83 | SD16 | semidirect |
| 218. #3078 | D83 | semidirect |
| 224. C83 | #10257 | semidirect |
| 313. C2×Q8 | #13050577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918775 | 2 |
| #24916935 | 2 |
| #24908400 | 2 |
| #24905918 | 2 |
| #24905913 | 2 |
| #24905337 | 2 |
| C83×#3078 | 2 |
| #10257 | 83 |