Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
950 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 111 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. #24918378 | C2 | semidirect |
| 2. #24915858 | C2 | semidirect |
| 3. #24906132 | C2 | semidirect |
| 4. #24905296 | C2 | semidirect |
| 5. C83×#1962 | C2 | semidirect |
| 31. C4⋊(C83⋊C8) | D4 | semidirect |
| 37. C4⋊Q8×C83 | D4 | semidirect |
| 38. #127×C83 | D4 | semidirect |
| 78. C42×C83 | D8 | semidirect |
| 138. #1962 | D83 | semidirect |
| 141. C83 | #10280 | semidirect |
| 162. C4⋊Q8 | D332 | semidirect |
| 170. #127 | D332 | semidirect |
| 214. C42 | #13050575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918378 | 2 |
| #24915858 | 2 |
| #24906132 | 2 |
| #24905296 | 2 |
| C83×#1962 | 2 |
| #10280 | 83 |