Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
130 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 130 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 |
|---|---|---|
| 1. C2×#17989787 | C2 | semidirect |
| 2. C2×#17989785 | C2 | semidirect |
| 3. #22627599 | C2 | semidirect |
| 4. #22627595 | C2 | semidirect |
| 5. #22627555 | C2 | semidirect |
| 6. #22627546 | C2 | semidirect |
| 7. #102×C293 | C2 | semidirect |
| 31. #14556873 | D4 | semidirect |
| 59. C293 | #469 | semidirect |
| 67. #102 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989787 | 2 |
| C2×#17989785 | 2 |
| #22627599 | 2 |
| #22627595 | 2 |
| #22627555 | 2 |
| #22627546 | 2 |
| #102×C293 | 2 |
| #469 | 293 |