Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 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. #22627672 | C2 | semidirect |
| 2. #22627671 | C2 | semidirect |
| 3. #22627657 | C2 | semidirect |
| 4. #22627656 | C2 | semidirect |
| 5. #22627653 | C2 | semidirect |
| 6. #22627645 | C2 | semidirect |
| 7. #22627644 | C2 | semidirect |
| 8. C2×#17989792 | C2 | semidirect |
| 9. Q16×D293 | C2 | semidirect |
| 10. #22627632 | C2 | semidirect |
| 11. #137×C293 | C2 | semidirect |
| 87. C293 | #578 | semidirect |
| 94. #137 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627672 | 2 |
| #22627671 | 2 |
| #22627657 | 2 |
| #22627656 | 2 |
| #22627653 | 2 |
| #22627645 | 2 |
| #22627644 | 2 |
| C2×#17989792 | 2 |
| Q16×D293 | 2 |
| #22627632 | 2 |
| #137×C293 | 2 |
| #578 | 293 |