Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
412 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 79 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. #24909275 | C2 | semidirect |
| 3. #24905503 | C2 | semidirect |
| 4. #24905499 | C2 | semidirect |
| 5. C83×#2165 | C2 | semidirect |
| 16. #19127522 | C22 | semidirect |
| 20. #364×C83 | C22 | semidirect |
| 152. #2165 | D83 | semidirect |
| 155. C83 | #11992 | semidirect |
| 168. #364 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917915 | 2 |
| #24909275 | 2 |
| #24905503 | 2 |
| #24905499 | 2 |
| C83×#2165 | 2 |
| #11992 | 83 |