Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
404 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 2. #23750493 | C2 | semidirect |
| 6. #18011990 | C4 | semidirect |
| 10. C2×C4×#10597010 | C4 | semidirect |
| 12. C2×#14558720 | C4 | semidirect |
| 16. C2×C8×D149 | C4 | semidirect |
| 17. C2×M16×C149 | C4 | semidirect |
| 24. C4×#10597010 | C2×C4 | semidirect |
| 37. C2×#11924746 | C2×C4 | semidirect |
| 42. C2×C8×C149 | C2×C4 | semidirect |
| 93. D149 | H(3,ℤ/4) | semidirect |
| 94. C149 | C2×H(3,ℤ/4) | semidirect |
| 104. C2×M16 | #10597010 | semidirect |
| 131. C2×C8 | C2×#10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011990 | 2 |
| #23750493 | 2 |
| C2×M16×D149 | 2 |
| C2×H(3,ℤ/4) | 149 |