Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
214 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22627617 | C2 | semidirect |
| 2. #22627615 | C2 | semidirect |
| 3. #22627614 | C2 | semidirect |
| 5. #22627600 | C2 | semidirect |
| 6. Q8×Dic293 | C2 | semidirect |
| 8. #22627583 | C2 | semidirect |
| 9. #22627582 | C2 | semidirect |
| 10. C4⋊C4×D293 | C2 | semidirect |
| 11. C22⋊Q8×C293 | C2 | semidirect |
| 72. C293 | #552 | semidirect |
| 79. C22⋊Q8 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627617 | 2 |
| #22627615 | 2 |
| #22627614 | 2 |
| #22627606 | 2 |
| #22627600 | 2 |
| Q8×Dic293 | 2 |
| C4×C22⋊D293 | 2 |
| #22627583 | 2 |
| #22627582 | 2 |
| C4⋊C4×D293 | 2 |
| C22⋊Q8×C293 | 2 |
| #552 | 293 |