Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
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. #22627619 | C2 | semidirect |
| 2. #22627615 | C2 | semidirect |
| 3. #22627614 | C2 | semidirect |
| 5. #22627604 | C2 | semidirect |
| 6. #22627603 | C2 | semidirect |
| 7. #22627589 | C2 | semidirect |
| 9. #22627583 | C2 | semidirect |
| 10. #22627582 | C2 | semidirect |
| 11. C2×C4⋊C4×C293 | C2 | semidirect |
| 72. C293 | #552 | semidirect |
| 84. C2×C4⋊C4 | 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 |
| #22627614 | 2 |
| #22627607 | 2 |
| #22627604 | 2 |
| #22627603 | 2 |
| #22627589 | 2 |
| C4×C22⋊D293 | 2 |
| #22627583 | 2 |
| #22627582 | 2 |
| C2×C4⋊C4×C293 | 2 |
| #552 | 293 |