Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
654 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 654 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. #24918466 | C2 | semidirect |
| 2. #24917563 | C2 | semidirect |
| 4. #24908407 | C2 | semidirect |
| 5. #24905907 | C2 | semidirect |
| 6. #24905318 | C2 | semidirect |
| 7. C83×#1527 | C2 | semidirect |
| 39. #14581792 | D4 | semidirect |
| 40. #14581792 | D4 | semidirect |
| 61. C4⋊(C83⋊C8) | D4 | semidirect |
| 82. #97×C83 | D4 | semidirect |
| 232. #1527 | D83 | semidirect |
| 235. C83 | #10008 | semidirect |
| 309. #97 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918466 | 2 |
| #24917563 | 2 |
| #24912403 | 2 |
| #24908407 | 2 |
| #24905907 | 2 |
| #24905318 | 2 |
| C83×#1527 | 2 |
| #10008 | 83 |