Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
934 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 159 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. C2×#19128078 | C2 | semidirect |
| 2. C2×#19128077 | C2 | semidirect |
| 3. #24908268 | C2 | semidirect |
| 4. C83⋊#1273 | C2 | semidirect |
| 5. C83×#1957 | C2 | semidirect |
| 63. C2×C83⋊C8 | D8 | semidirect |
| 78. C2×C8×C83 | D8 | semidirect |
| 152. #1957 | D83 | semidirect |
| 154. C83 | #10304 | semidirect |
| 227. C2×C8 | #13050575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128078 | 2 |
| C2×#19128077 | 2 |
| #24908268 | 2 |
| C83⋊#1273 | 2 |
| C83×#1957 | 2 |
| #10304 | 83 |