Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
598 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 598 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 |
|---|---|---|
| 2. #24918584 | C2 | semidirect |
| 3. #24908416 | C2 | semidirect |
| 4. #24908382 | C2 | semidirect |
| 5. #24905958 | C2 | semidirect |
| 6. #24905314 | C2 | semidirect |
| 7. C83×#3152 | C2 | semidirect |
| 117. M16×C83 | D8 | semidirect |
| 206. #3152 | D83 | semidirect |
| 211. C83 | #10204 | semidirect |
| 311. M16 | #13050575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918770 | 2 |
| #24918584 | 2 |
| #24908416 | 2 |
| #24908382 | 2 |
| #24905958 | 2 |
| #24905314 | 2 |
| C83×#3152 | 2 |
| #10204 | 83 |