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 |
|---|---|---|
| 3. #24905289 | C2 | semidirect |
| 4. #24905286 | C2 | semidirect |
| 5. C83×#2734 | C2 | semidirect |
| 86. C4⋊C4×C83 | SD16 | semidirect |
| 152. #2734 | D83 | semidirect |
| 157. C83 | #7741 | semidirect |
| 238. C4⋊C4 | #13050577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24908697 | 2 |
| #24908550 | 2 |
| #24905289 | 2 |
| #24905286 | 2 |
| C83×#2734 | 2 |
| #7741 | 83 |