Finite Group DatabasebetaFinite Group DatabasebetaOrder 14912.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #21418530 | C2 | semidirect |
| 2. #21418528 | C2 | semidirect |
| 3. #21418525 | C2 | semidirect |
| 4. #21418521 | C2 | semidirect |
| 5. #21418519 | C2 | semidirect |
| 6. #21418516 | C2 | semidirect |
| 7. #21418512 | C2 | semidirect |
| 9. C4×Dic466 | C2 | semidirect |
| 10. C4×C22⋊D233 | C2 | semidirect |
| 11. C4×C22⋊D233 | C2 | semidirect |
| 12. #21418494 | C2 | semidirect |
| 13. #21418492 | C2 | semidirect |
| 14. C2×C4×Dic233 | C2 | semidirect |
| 15. C4×D4×C233 | C2 | semidirect |
| 103. C233 | #529 | semidirect |
| 116. C4×D4 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21418530 | 2 |
| #21418528 | 2 |
| #21418525 | 2 |
| #21418521 | 2 |
| #21418519 | 2 |
| #21418516 | 2 |
| #21418512 | 2 |
| #21418507 | 2 |
| C4×Dic466 | 2 |
| C4×C22⋊D233 | 2 |
| #21418494 | 2 |
| #21418492 | 2 |
| C2×C4×Dic233 | 2 |
| C4×D4×C233 | 2 |
| #529 | 233 |