Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19127534 | C2 | semidirect |
| 3. #366×D83 | C2 | semidirect |
| 4. #24905645 | C2 | semidirect |
| 5. #24905643 | C2 | semidirect |
| 6. #24905641 | C2 | semidirect |
| 7. C83×#1415 | C2 | semidirect |
| 10. #19128130 | C4 | semidirect |
| 30. Dic664 | C2×C4 | semidirect |
| 40. D16×C83 | C2×C4 | semidirect |
| 111. #1415 | D83 | semidirect |
| 112. C83 | #13616 | semidirect |
| 139. D16 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128130 | 2 |
| C2×#19127534 | 2 |
| #366×D83 | 2 |
| #24905645 | 2 |
| #24905643 | 2 |
| #24905641 | 2 |
| C83×#1415 | 2 |
| #13616 | 83 |