Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 39 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. #22627657 | C2 | semidirect |
| 3. #22627654 | C2 | semidirect |
| 4. #22627624 | C2 | semidirect |
| 5. #22627552 | C2 | semidirect |
| 6. #22627542 | C2 | semidirect |
| 7. #104×C293 | C2 | semidirect |
| 61. C293 | #456 | semidirect |
| 68. #104 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627671 | 2 |
| #22627657 | 2 |
| #22627654 | 2 |
| #22627624 | 2 |
| #22627552 | 2 |
| #22627542 | 2 |
| #104×C293 | 2 |
| #456 | 293 |