Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
174 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 55 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×#18012680 | C2 | semidirect |
| 2. C22×C151⋊C16 | C2 | semidirect |
| 3. #23752448 | C2 | semidirect |
| 4. #23752037 | C2 | semidirect |
| 5. #23752013 | C2 | semidirect |
| 6. #23752012 | C2 | semidirect |
| 7. #466×C151 | C2 | semidirect |
| 28. C151⋊C16 | D4 | semidirect |
| 63. C22×C151 | D16 | semidirect |
| 79. C151 | #2215 | semidirect |
| 84. #466 | D151 | semidirect |
| 146. C22 | #18012680 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012680 | 2 |
| C22×C151⋊C16 | 2 |
| #23752448 | 2 |
| #23752037 | 2 |
| #23752013 | 2 |
| #23752012 | 2 |
| #466×C151 | 2 |
| #2215 | 151 |