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. C2×#19128139 | C2 | semidirect |
| 2. #24917183 | C2 | semidirect |
| 3. #24917111 | C2 | semidirect |
| 4. C2×#19127515 | C2 | semidirect |
| 5. #24909200 | C2 | semidirect |
| 6. #24905578 | C2 | semidirect |
| 7. C83×#2117 | C2 | semidirect |
| 42. C2×Dic332 | D4 | semidirect |
| 50. C2×D664 | D4 | semidirect |
| 60. #14581728 | D4 | semidirect |
| 78. M32×C83 | D4 | semidirect |
| 217. #2117 | D83 | semidirect |
| 219. C83 | #13310 | 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 |
|---|---|
| C2×#19128139 | 2 |
| #24917183 | 2 |
| #24917111 | 2 |
| C2×#19127515 | 2 |
| #24909200 | 2 |
| #24905578 | 2 |
| C83×#2117 | 2 |
| #13310 | 83 |