Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
770 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 770 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. #24918450 | C2 | semidirect |
| 2. #24917915 | C2 | semidirect |
| 3. #24913571 | C2 | semidirect |
| 4. #24906176 | C2 | semidirect |
| 5. #24905972 | C2 | semidirect |
| 6. #24905357 | C2 | semidirect |
| 7. C83×#1527 | C2 | semidirect |
| 41. #14581792 | D4 | semidirect |
| 46. #14581789 | D4 | semidirect |
| 56. C4⋊(C83⋊C8) | D4 | semidirect |
| 76. #97×C83 | D4 | semidirect |
| 216. #1527 | D83 | semidirect |
| 219. C83 | #10088 | semidirect |
| 286. #97 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918450 | 2 |
| #24917915 | 2 |
| #24913571 | 2 |
| #24906176 | 2 |
| #24905972 | 2 |
| #24905357 | 2 |
| C83×#1527 | 2 |
| #10088 | 83 |