Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
302 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 107 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×#19127527 | C2 | semidirect |
| 3. #24905645 | C2 | semidirect |
| 4. #24905642 | C2 | semidirect |
| 5. C2×M64×C83 | C2 | semidirect |
| 8. #19128133 | C4 | semidirect |
| 26. Dic664 | C2×C4 | semidirect |
| 29. D1328 | C2×C4 | semidirect |
| 97. C2×M64 | D83 | semidirect |
| 101. C83 | #13616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128133 | 2 |
| C2×#19127527 | 2 |
| #24905645 | 2 |
| #24905642 | 2 |
| C2×M64×C83 | 2 |
| #13616 | 83 |