Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
306 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 99 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. #24909218 | C2 | semidirect |
| 5. #24905549 | C2 | semidirect |
| 6. #24905544 | C2 | semidirect |
| 7. C83×#2110 | C2 | semidirect |
| 146. #2110 | D83 | semidirect |
| 150. C83 | #13129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909218 | 2 |
| #24909090 | 2 |
| #24909083 | 2 |
| #24907302 | 2 |
| #24905549 | 2 |
| #24905544 | 2 |
| C83×#2110 | 2 |
| #13129 | 83 |