Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
678 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 678 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. #24918584 | C2 | semidirect |
| 3. #24908291 | C2 | semidirect |
| 4. #24906135 | C2 | semidirect |
| 5. #24906131 | C2 | semidirect |
| 6. #24905296 | C2 | semidirect |
| 7. C83×#2858 | C2 | semidirect |
| 117. C42×C83 | D8 | semidirect |
| 194. #2858 | D83 | semidirect |
| 199. C83 | #10284 | semidirect |
| 309. C42 | #13050575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918584 | 2 |
| #24918381 | 2 |
| #24908291 | 2 |
| #24906135 | 2 |
| #24906131 | 2 |
| #24905296 | 2 |
| C83×#2858 | 2 |
| #10284 | 83 |