Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
1488 conjugacy classes of subgroups; only the 762 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 762 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. #23750693 | C2 | direct (N × H) |
| 2. C2×Q8×#10597010 | C2 | semidirect |
| 5. Q8×#10597010 | C22 | semidirect |
| 10. C22×Dic298 | C4 | semidirect |
| 11. C2×Q8×D149 | C4 | semidirect |
| 12. C2×Q8×D149 | C4 | semidirect |
| 16. C22×Q8×C149 | C4 | semidirect |
| 23. C2×Dic298 | C2×C4 | semidirect |
| 25. Q8×D149 | C2×C4 | semidirect |
| 33. C2×Q8×C149 | C2×C4 | semidirect |
| 66. C2×C149 | #519 | semidirect |
| 69. D149 | #519 | semidirect |
| 71. C149 | C2×#519 | semidirect |
| 82. C22×Q8 | #10597010 | semidirect |
| 96. C2×Q8 | C2×#10597010 | semidirect |
| 141. C2 | #23750693 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750693 | 2 |
| C2×Q8×#10597010 | 2 |
| C2×#18011990 | 2 |
| C22×Q8×D149 | 2 |
| C2×#519 | 149 |