Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
466 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 109 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. #24920565 | C2 | semidirect |
| 3. #24909191 | C2 | semidirect |
| 4. #24907510 | C2 | semidirect |
| 5. #24905563 | C2 | semidirect |
| 6. #24905562 | C2 | semidirect |
| 7. C83×#2143 | C2 | semidirect |
| 45. C2×C83⋊C16 | D4 | semidirect |
| 67. C2×C16×C83 | D4 | semidirect |
| 184. #2143 | D83 | semidirect |
| 188. C83 | #13076 | semidirect |
| 240. C2×C16 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920565 | 2 |
| #24917121 | 2 |
| #24909191 | 2 |
| #24907510 | 2 |
| #24905563 | 2 |
| #24905562 | 2 |
| C83×#2143 | 2 |
| #13076 | 83 |