Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23752762 | C2 | semidirect |
| 2. #23752746 | C2 | semidirect |
| 3. #23752513 | C2 | semidirect |
| 4. #23752508 | C2 | semidirect |
| 5. #23752503 | C2 | semidirect |
| 6. #23752448 | C2 | semidirect |
| 7. #23752441 | C2 | semidirect |
| 8. #23752428 | C2 | semidirect |
| 9. #23752413 | C2 | semidirect |
| 10. #23752408 | C2 | semidirect |
| 11. C2×C4⋊C8×C151 | C2 | semidirect |
| 141. C151 | #3247 | semidirect |
| 153. C2×C4⋊C8 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752762 | 2 |
| #23752746 | 2 |
| #23752513 | 2 |
| #23752508 | 2 |
| #23752503 | 2 |
| #23752448 | 2 |
| #23752441 | 2 |
| #23752428 | 2 |
| #23752413 | 2 |
| #23752408 | 2 |
| C2×C4⋊C8×C151 | 2 |
| #3247 | 151 |