Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
288 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 59 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. C2×#19127538 | C2 | semidirect |
| 3. #24909551 | C2 | semidirect |
| 4. #24905644 | C2 | semidirect |
| 5. #24905642 | C2 | semidirect |
| 6. (C2×D83)⋊C32 | C2 | semidirect |
| 7. C2×Q64×C83 | C2 | semidirect |
| 112. C2×Q64 | D83 | semidirect |
| 118. C83 | #13666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128134 | 2 |
| C2×#19127538 | 2 |
| #24909551 | 2 |
| #24905644 | 2 |
| #24905642 | 2 |
| (C2×D83)⋊C32 | 2 |
| C2×Q64×C83 | 2 |
| #13666 | 83 |