Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
594 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #24908445 | C2 | semidirect |
| 5. #24905321 | C2 | semidirect |
| 6. #24905291 | C2 | semidirect |
| 7. C83×#1518 | C2 | semidirect |
| 10. #19128075 | C4 | semidirect |
| 11. #19128049 | C4 | semidirect |
| 49. C4×C83⋊C8 | C2×C4 | semidirect |
| 52. C4⋊Q8×C83 | C2×C4 | semidirect |
| 53. C4⋊Q8×C83 | C2×C4 | semidirect |
| 96. C4×Dic83 | SD16 | semidirect |
| 199. #1518 | D83 | semidirect |
| 202. C83 | #9295 | semidirect |
| 228. C4⋊Q8 | C4×D83 | semidirect |
| 229. C4⋊Q8 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918401 | 2 |
| #24910186 | 2 |
| #24908445 | 2 |
| #24906130 | 2 |
| #24905321 | 2 |
| #24905291 | 2 |
| C83×#1518 | 2 |
| #9295 | 83 |