Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23752757 | C2 | semidirect |
| 2. #23752616 | C2 | semidirect |
| 3. #23752587 | C2 | semidirect |
| 4. #23752557 | C2 | semidirect |
| 5. #23752448 | C2 | semidirect |
| 6. #23752446 | C2 | semidirect |
| 7. D8×Dic151 | C2 | semidirect |
| 8. #23752294 | C2 | semidirect |
| 9. #23752292 | C2 | semidirect |
| 10. C2×C8×Dic151 | C2 | semidirect |
| 11. #466×C151 | C2 | semidirect |
| 82. C2×Dic151 | D8 | semidirect |
| 89. C151⋊C8 | #41 | semidirect |
| 101. C8×C151 | #41 | semidirect |
| 127. C151 | #3169 | semidirect |
| 135. #466 | D151 | semidirect |
| 229. C8 | #14559003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752757 | 2 |
| #23752616 | 2 |
| #23752587 | 2 |
| #23752557 | 2 |
| #23752448 | 2 |
| #23752446 | 2 |
| D8×Dic151 | 2 |
| #23752294 | 2 |
| #23752292 | 2 |
| C2×C8×Dic151 | 2 |
| #466×C151 | 2 |
| #3169 | 151 |