Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
684 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 85 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. #24917839 | C2 | semidirect |
| 3. #24906176 | C2 | semidirect |
| 4. #24906061 | C2 | semidirect |
| 5. #24905975 | C2 | semidirect |
| 6. #24905355 | C2 | semidirect |
| 7. C83×#3215 | C2 | semidirect |
| 49. #14581703 | D4 | semidirect |
| 57. C4⋊Q8×C83 | D4 | semidirect |
| 58. C4⋊Q8×C83 | D4 | semidirect |
| 72. C4⋊C8×C83 | D4 | semidirect |
| 201. #3215 | D83 | semidirect |
| 208. C83 | #10096 | semidirect |
| 241. C4⋊Q8 | C22⋊D83 | semidirect |
| 242. C4⋊Q8 | C22⋊D83 | semidirect |
| 265. C4⋊C8 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917839 | 2 |
| #24913571 | 2 |
| #24906176 | 2 |
| #24906061 | 2 |
| #24905975 | 2 |
| #24905355 | 2 |
| C83×#3215 | 2 |
| #10096 | 83 |