Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
594 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 594 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. C2×#19128139 | C2 | semidirect |
| 2. C2×#19128136 | C2 | semidirect |
| 3. #24917906 | C2 | semidirect |
| 4. C2×#19127510 | C2 | semidirect |
| 5. #24908337 | C2 | semidirect |
| 6. #24905546 | C2 | semidirect |
| 7. C2×#360×C83 | C2 | semidirect |
| 52. C2×D664 | D4 | semidirect |
| 68. #14581732 | D4 | semidirect |
| 84. M32×C83 | D4 | semidirect |
| 233. C2×#360 | D83 | semidirect |
| 236. C83 | #13341 | semidirect |
| 309. 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 |
| C2×#19128136 | 2 |
| #24917906 | 2 |
| C2×#19127510 | 2 |
| #24908337 | 2 |
| #24905546 | 2 |
| C2×#360×C83 | 2 |
| #13341 | 83 |