Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
466 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19127514 | C2 | semidirect |
| 3. #24909198 | C2 | semidirect |
| 4. #24909192 | C2 | semidirect |
| 5. #24909067 | C2 | semidirect |
| 6. #24907586 | C2 | semidirect |
| 7. C83×#2140 | C2 | semidirect |
| 13. #19128084 | C4 | semidirect |
| 14. #19128076 | C4 | semidirect |
| 47. #14581732 | D4 | semidirect |
| 64. C2×C16×C83 | D4 | semidirect |
| 179. #2140 | D83 | semidirect |
| 182. C83 | #13215 | semidirect |
| 235. C2×C16 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917944 | 2 |
| C2×#19127514 | 2 |
| #24909198 | 2 |
| #24909192 | 2 |
| #24909067 | 2 |
| #24907586 | 2 |
| C83×#2140 | 2 |
| #13215 | 83 |