Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
536 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. C2×#19128142 | C2 | semidirect |
| 3. #24917952 | C2 | semidirect |
| 4. #24909198 | C2 | semidirect |
| 5. #24908359 | C2 | semidirect |
| 6. #24905548 | C2 | semidirect |
| 7. C83×#2141 | C2 | semidirect |
| 216. #2141 | D83 | semidirect |
| 219. C83 | #13335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920599 | 2 |
| C2×#19128142 | 2 |
| #24917952 | 2 |
| #24909198 | 2 |
| #24908359 | 2 |
| #24905548 | 2 |
| C83×#2141 | 2 |
| #13335 | 83 |