Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
528 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 528 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 |
|---|---|---|
| 2. #24917268 | C2 | semidirect |
| 4. #24905919 | C2 | semidirect |
| 6. #24905338 | C2 | semidirect |
| 7. C83×#1984 | C2 | semidirect |
| 122. C2×Q8×C83 | SD16 | semidirect |
| 220. #1984 | D83 | semidirect |
| 224. C83 | #10257 | semidirect |
| 313. C2×Q8 | #13050579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918780 | 2 |
| #24917268 | 2 |
| #24916935 | 2 |
| #24905919 | 2 |
| #24905915 | 2 |
| #24905338 | 2 |
| C83×#1984 | 2 |
| #10257 | 83 |