Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. #24905827 | C2 | semidirect |
| 5. #24905351 | C2 | semidirect |
| 6. #24905306 | C2 | semidirect |
| 7. C2×#328×C83 | C2 | semidirect |
| 10. #19128031 | C4 | semidirect |
| 11. #19128014 | C4 | semidirect |
| 15. #19127857 | C4 | semidirect |
| 16. #19127840 | C4 | semidirect |
| 237. C2×#328 | D83 | semidirect |
| 241. C83 | #9263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918244 | 2 |
| #24916517 | 2 |
| #24905965 | 2 |
| #24905827 | 2 |
| #24905351 | 2 |
| #24905306 | 2 |
| C2×#328×C83 | 2 |
| #9263 | 83 |