Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
620 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 113 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. #24910371 | C2 | semidirect |
| 3. #24905958 | C2 | semidirect |
| 4. #24905855 | C2 | semidirect |
| 5. #24905365 | C2 | semidirect |
| 6. #24905321 | C2 | semidirect |
| 7. C83×#1517 | C2 | semidirect |
| 12. #19127903 | C4 | semidirect |
| 13. #19127893 | C4 | semidirect |
| 51. C4⋊(C83⋊C8) | C2×C4 | semidirect |
| 60. C4⋊Q8×C83 | C2×C4 | semidirect |
| 61. #127×C83 | C2×C4 | semidirect |
| 217. #1517 | D83 | semidirect |
| 222. C83 | #9179 | semidirect |
| 253. C4⋊Q8 | C4×D83 | semidirect |
| 254. #127 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916923 | 2 |
| #24910371 | 2 |
| #24905958 | 2 |
| #24905855 | 2 |
| #24905365 | 2 |
| #24905321 | 2 |
| C83×#1517 | 2 |
| #9179 | 83 |