Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24910573 | C2 | semidirect |
| 3. #24906086 | C2 | semidirect |
| 4. #24905971 | C2 | semidirect |
| 5. #24905356 | C2 | semidirect |
| 6. #24905355 | C2 | semidirect |
| 7. C83×#1505 | C2 | semidirect |
| 11. #19128093 | C4 | semidirect |
| 12. #19128088 | C4 | semidirect |
| 58. #14581703 | C2×C4 | semidirect |
| 66. C4⋊Q8×C83 | C2×C4 | semidirect |
| 67. #127×C83 | C2×C4 | semidirect |
| 231. #1505 | D83 | semidirect |
| 234. C83 | #9441 | semidirect |
| 271. C4⋊Q8 | C4×D83 | semidirect |
| 272. #127 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917931 | 2 |
| #24910573 | 2 |
| #24906086 | 2 |
| #24905971 | 2 |
| #24905356 | 2 |
| #24905355 | 2 |
| C83×#1505 | 2 |
| #9441 | 83 |