Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
174 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 50 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. D8×#10597010 | C2 | semidirect |
| 2. #23750551 | C2 | semidirect |
| 3. #23750537 | C2 | semidirect |
| 4. C16×#10597010 | C2 | semidirect |
| 12. D2384 | C4 | semidirect |
| 13. #18011852 | C4 | semidirect |
| 15. D16×C149 | C4 | semidirect |
| 23. D1192 | C2×C4 | semidirect |
| 26. #14558711 | C2×C4 | semidirect |
| 27. D8×C149 | C2×C4 | semidirect |
| 28. C16×C149 | C2×C4 | semidirect |
| 48. #10597010 | D16 | direct (N × H) |
| 56. C149 | C4×D16 | semidirect |
| 67. D16 | #10597010 | direct (N × H) |
| 77. D8 | C2×#10597010 | semidirect |
| 85. C16 | C2×#10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×#10597010 | 2 |
| #23750551 | 2 |
| #23750537 | 2 |
| C16×#10597010 | 2 |
| D16×D149 | 2 |
| C4×D16 | 149 |