Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
242 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #24905536 | C2 | semidirect |
| 5. #24905535 | C2 | semidirect |
| 6. #24905534 | C2 | semidirect |
| 7. C83×#1372 | C2 | semidirect |
| 28. #14581731 | C8 | semidirect |
| 59. C83⋊C16 | C2×C8 | semidirect |
| 66. C16×C83 | C2×C8 | semidirect |
| 109. #1372 | D83 | semidirect |
| 112. C83 | #12009 | semidirect |
| 171. C16 | C8×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14581731 | 2 |
| #24906210 | 2 |
| #335×D83 | 2 |
| #24905536 | 2 |
| #24905535 | 2 |
| #24905534 | 2 |
| C83×#1372 | 2 |
| #12009 | 83 |