Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
890 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 135 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. #24909200 | C2 | semidirect |
| 3. #24909171 | C2 | semidirect |
| 4. #24907509 | C2 | semidirect |
| 5. C83×#2113 | C2 | semidirect |
| 11. #19128501 | C4 | semidirect |
| 14. #19127739 | C22 | semidirect |
| 21. C2×M32×C83 | C22 | semidirect |
| 22. C22×C16×C83 | C22 | semidirect |
| 171. #2113 | D83 | semidirect |
| 173. C83 | #12745 | semidirect |
| 183. C2×M32 | C2×D83 | semidirect |
| 184. C22×C16 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24922237 | 2 |
| #24909200 | 2 |
| #24909171 | 2 |
| #24907509 | 2 |
| C83×#2113 | 2 |
| #12745 | 83 |