Finite Group DatabasebetaFinite Group DatabasebetaOrder 14912.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21418526 | C2 | semidirect |
| 3. #21418526 | C2 | semidirect |
| 5. #21418511 | C2 | semidirect |
| 6. Q8×Dic233 | C2 | semidirect |
| 8. #21418493 | C2 | semidirect |
| 9. #21418491 | C2 | semidirect |
| 10. C2×C4⋊Dic233 | C2 | semidirect |
| 11. C22⋊Q8×C233 | C2 | semidirect |
| 72. C233 | #552 | semidirect |
| 79. C22⋊Q8 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21418530 | 2 |
| #21418526 | 2 |
| #21418519 | 2 |
| #21418511 | 2 |
| Q8×Dic233 | 2 |
| C4×C22⋊D233 | 2 |
| #21418493 | 2 |
| #21418491 | 2 |
| C2×C4⋊Dic233 | 2 |
| C22⋊Q8×C233 | 2 |
| #552 | 233 |