Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 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 |
|---|---|---|
| 1. #24917179 | C2 | semidirect |
| 2. #24917107 | C2 | semidirect |
| 3. C2×#19127514 | C2 | semidirect |
| 4. #24909199 | C2 | semidirect |
| 5. #24909092 | C2 | semidirect |
| 6. #24905578 | C2 | semidirect |
| 7. C2×#509×C83 | C2 | semidirect |
| 54. #14581728 | D4 | semidirect |
| 66. C2×Q16×C83 | D4 | semidirect |
| 74. C2×D8×C83 | D4 | semidirect |
| 79. M32×C83 | D4 | semidirect |
| 212. C2×#509 | D83 | semidirect |
| 219. C83 | #13310 | semidirect |
| 255. C2×Q16 | C22⋊D83 | semidirect |
| 263. C2×D8 | C22⋊D83 | semidirect |
| 283. M32 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917179 | 2 |
| #24917107 | 2 |
| C2×#19127514 | 2 |
| #24909199 | 2 |
| #24909092 | 2 |
| #24905578 | 2 |
| C2×#509×C83 | 2 |
| #13310 | 83 |