Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
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. #22627619 | C2 | semidirect |
| 2. #22627615 | C2 | semidirect |
| 3. #22627613 | C2 | semidirect |
| 4. #22627608 | C2 | semidirect |
| 6. Q8×Dic293 | C2 | semidirect |
| 7. #22627586 | C2 | semidirect |
| 8. #22627584 | C2 | semidirect |
| 9. #22627582 | C2 | semidirect |
| 10. C2×C4×Dic293 | C2 | semidirect |
| 11. C22⋊Q8×C293 | C2 | semidirect |
| 74. C293 | #529 | semidirect |
| 80. C22⋊Q8 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627619 | 2 |
| #22627615 | 2 |
| #22627613 | 2 |
| #22627608 | 2 |
| #22627598 | 2 |
| Q8×Dic293 | 2 |
| #22627586 | 2 |
| #22627584 | 2 |
| #22627582 | 2 |
| C2×C4×Dic293 | 2 |
| C22⋊Q8×C293 | 2 |
| #529 | 293 |