Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
640 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 113 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. #24918609 | C2 | semidirect |
| 4. #24908440 | C2 | semidirect |
| 5. #24906134 | C2 | semidirect |
| 7. C83×#1276 | C2 | semidirect |
| 114. C42×C83 | SD16 | semidirect |
| 187. #1276 | D83 | semidirect |
| 188. C83 | #10294 | semidirect |
| 295. C42 | #13050579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918609 | 2 |
| #24918406 | 2 |
| #24915820 | 2 |
| #24908440 | 2 |
| #24906134 | 2 |
| #24906130 | 2 |
| C83×#1276 | 2 |
| #10294 | 83 |