Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
650 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #24909825 | C2 | semidirect |
| 3. #24908383 | C2 | semidirect |
| 4. #24905905 | C2 | semidirect |
| 5. #24905356 | C2 | semidirect |
| 6. #24905318 | C2 | semidirect |
| 7. C83×#1505 | C2 | semidirect |
| 11. #19127988 | C4 | semidirect |
| 12. #19127893 | C4 | semidirect |
| 46. C4⋊(C83⋊C8) | C2×C4 | semidirect |
| 57. C4⋊Q8×C83 | C2×C4 | semidirect |
| 58. #127×C83 | C2×C4 | semidirect |
| 158. D332 | #104 | semidirect |
| 200. #1505 | D83 | semidirect |
| 204. C83 | #9325 | semidirect |
| 232. C4⋊Q8 | C4×D83 | semidirect |
| 233. #127 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917550 | 2 |
| #24909825 | 2 |
| #24908383 | 2 |
| #24905905 | 2 |
| #24905356 | 2 |
| #24905318 | 2 |
| C83×#1505 | 2 |
| #9325 | 83 |