Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
204 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 1. C2×#19127538 | C2 | semidirect |
| 2. C22×C83⋊C32 | C2 | semidirect |
| 4. #24905664 | C2 | semidirect |
| 5. #24905644 | C2 | semidirect |
| 6. #24905640 | C2 | semidirect |
| 7. C83×#2216 | C2 | semidirect |
| 28. C83⋊C32 | D4 | semidirect |
| 79. C22×C83 | SD64 | semidirect |
| 98. #2216 | D83 | semidirect |
| 103. C83 | #13696 | semidirect |
| 178. C22 | #19127538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127538 | 2 |
| C22×C83⋊C32 | 2 |
| #24909549 | 2 |
| #24905664 | 2 |
| #24905644 | 2 |
| #24905640 | 2 |
| C83×#2216 | 2 |
| #13696 | 83 |