Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
354 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 93 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×#19127521 | C2 | semidirect |
| 5. #24908212 | C2 | semidirect |
| 6. #24905571 | C2 | semidirect |
| 7. C83×#2159 | C2 | semidirect |
| 147. #2159 | D83 | semidirect |
| 154. C83 | #13478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127521 | 2 |
| C2×#19127515 | 2 |
| #24909178 | 2 |
| #24908327 | 2 |
| #24908212 | 2 |
| #24905571 | 2 |
| C83×#2159 | 2 |
| #13478 | 83 |