Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
560 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 560 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 |
|---|---|---|
| 4. #24905866 | C2 | semidirect |
| 5. #24905787 | C2 | semidirect |
| 6. #24905358 | C2 | semidirect |
| 7. C83×#3078 | C2 | semidirect |
| 104. C2×Q8×C83 | SD16 | semidirect |
| 204. #3078 | D83 | semidirect |
| 210. C83 | #10179 | semidirect |
| 288. C2×Q8 | #13050577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918401 | 2 |
| C2×#19127901 | 2 |
| #24906132 | 2 |
| #24905866 | 2 |
| #24905787 | 2 |
| #24905358 | 2 |
| C83×#3078 | 2 |
| #10179 | 83 |