Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
304 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 83 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. #24909279 | C2 | semidirect |
| 2. #24907218 | C2 | semidirect |
| 3. #24905457 | C2 | semidirect |
| 5. #24905451 | C2 | semidirect |
| 17. #498×C83 | C4 | semidirect |
| 18. #495×C83 | C4 | semidirect |
| 23. #442×C83 | C4 | semidirect |
| 24. #441×C83 | C4 | semidirect |
| 152. C83 | #11769 | semidirect |
| 154. #498 | Dic83 | semidirect |
| 155. #495 | Dic83 | semidirect |
| 160. #442 | Dic83 | semidirect |
| 161. #441 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909279 | 2 |
| #24907218 | 2 |
| #24905457 | 2 |
| #24905454 | 2 |
| #24905451 | 2 |
| #24905448 | 2 |
| C83×#3173 | 2 |
| #11769 | 83 |