Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
572 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×D1328 | C2 | semidirect |
| 2. C2×#19127971 | C2 | semidirect |
| 3. #24917111 | C2 | semidirect |
| 4. C2×#19127515 | C2 | semidirect |
| 5. #24909180 | C2 | semidirect |
| 6. #24905559 | C2 | semidirect |
| 7. C2×#350×C83 | C2 | semidirect |
| 45. C2×D664 | D4 | semidirect |
| 55. #14581728 | D4 | semidirect |
| 74. C2×C16×C83 | D4 | semidirect |
| 205. C2×#350 | D83 | semidirect |
| 207. C83 | #13319 | semidirect |
| 268. C2×C16 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1328 | 2 |
| C2×#19127971 | 2 |
| #24917111 | 2 |
| C2×#19127515 | 2 |
| #24909180 | 2 |
| #24905559 | 2 |
| C2×#350×C83 | 2 |
| #13319 | 83 |