Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
950 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 109 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. #24915857 | C2 | semidirect |
| 3. #24908292 | C2 | semidirect |
| 4. #24906131 | C2 | semidirect |
| 5. #24906130 | C2 | semidirect |
| 6. #24905295 | C2 | semidirect |
| 7. C83×#3205 | C2 | semidirect |
| 48. C4⋊(C83⋊C8) | D4 | semidirect |
| 58. C4⋊Q8×C83 | D4 | semidirect |
| 63. #127×C83 | D4 | semidirect |
| 70. C4⋊C8×C83 | D4 | semidirect |
| 96. C4×Dic83 | D8 | semidirect |
| 211. #3205 | D83 | semidirect |
| 217. C83 | #10280 | semidirect |
| 250. C4⋊Q8 | C22⋊D83 | semidirect |
| 263. #127 | C22⋊D83 | semidirect |
| 276. C4⋊C8 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918378 | 2 |
| #24915857 | 2 |
| #24908292 | 2 |
| #24906131 | 2 |
| #24906130 | 2 |
| #24905295 | 2 |
| C83×#3205 | 2 |
| #10280 | 83 |