Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
492 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#14558992 | C2 | semidirect |
| 2. C2×#18012747 | C2 | semidirect |
| 3. #23752788 | C2 | semidirect |
| 5. #23752457 | C2 | semidirect |
| 6. #23752440 | C2 | semidirect |
| 7. #23752248 | C2 | semidirect |
| 8. #23752222 | C2 | semidirect |
| 9. #418×C151 | C2 | semidirect |
| 16. C2×#14558987 | C22 | semidirect |
| 18. C2×C8×D151 | C22 | semidirect |
| 24. #18012719 | C22 | semidirect |
| 28. #18012672 | C22 | semidirect |
| 29. #18012670 | C22 | semidirect |
| 30. #18012664 | C22 | semidirect |
| 50. C2×C151⋊C8 | D4 | semidirect |
| 120. C151 | #3057 | semidirect |
| 130. #418 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558992 | 2 |
| C2×#18012747 | 2 |
| #23752788 | 2 |
| #23752779 | 2 |
| #23752457 | 2 |
| #23752440 | 2 |
| #23752248 | 2 |
| #23752222 | 2 |
| #418×C151 | 2 |
| #3057 | 151 |