Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. C2×Q8×D293 | C2 | semidirect |
| 3. #22627623 | C2 | semidirect |
| 4. #22627610 | C2 | semidirect |
| 5. #22627609 | C2 | semidirect |
| 6. #22627606 | C2 | semidirect |
| 7. #22627604 | C2 | semidirect |
| 8. #22627603 | C2 | semidirect |
| 9. #22627600 | C2 | semidirect |
| 10. #22627582 | C2 | semidirect |
| 11. C22⋊Q8×C293 | C2 | semidirect |
| 83. C293 | #536 | semidirect |
| 94. C22⋊Q8 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989802 | 2 |
| C2×Q8×D293 | 2 |
| #22627623 | 2 |
| #22627610 | 2 |
| #22627609 | 2 |
| #22627606 | 2 |
| #22627604 | 2 |
| #22627603 | 2 |
| #22627600 | 2 |
| #22627582 | 2 |
| C22⋊Q8×C293 | 2 |
| #536 | 293 |