Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
294 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. #24905515 | C2 | semidirect |
| 5. #24905445 | C2 | semidirect |
| 6. #24905433 | C2 | semidirect |
| 7. C83×#3390 | C2 | semidirect |
| 75. Q16×C83 | SD16 | semidirect |
| 140. #3390 | D83 | semidirect |
| 147. C83 | #12361 | semidirect |
| 208. Q16 | #13050577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909706 | 2 |
| #24909503 | 2 |
| #24906947 | 2 |
| #24905515 | 2 |
| #24905445 | 2 |
| #24905433 | 2 |
| C83×#3390 | 2 |
| #12361 | 83 |