Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
554 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 554 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. #24906144 | C2 | semidirect |
| 5. #24905858 | C2 | semidirect |
| 6. #24905366 | C2 | semidirect |
| 7. C83×#2568 | C2 | semidirect |
| 107. C2×Q8×C83 | SD16 | semidirect |
| 206. #2568 | D83 | semidirect |
| 211. C83 | #10244 | semidirect |
| 294. C2×Q8 | #13050577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918388 | 2 |
| #24916935 | 2 |
| #24906144 | 2 |
| #24905957 | 2 |
| #24905858 | 2 |
| #24905366 | 2 |
| C83×#2568 | 2 |
| #10244 | 83 |