Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 44 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. #23750672 | C2 | semidirect |
| 2. #23750666 | C2 | semidirect |
| 3. #23750550 | C2 | semidirect |
| 4. #23750543 | C2 | semidirect |
| 5. #23750541 | C2 | semidirect |
| 6. #23750516 | C2 | semidirect |
| 18. #18011856 | C4 | semidirect |
| 19. #18011855 | C4 | semidirect |
| 20. #18011852 | C4 | semidirect |
| 22. D16×C149 | C4 | semidirect |
| 34. Dic596 | C2×C4 | semidirect |
| 39. #14558711 | C2×C4 | semidirect |
| 41. D8×C149 | C2×C4 | semidirect |
| 42. C16×C149 | C2×C4 | semidirect |
| 75. C149 | AGL(1,ℤ/16) | semidirect |
| 91. D16 | #10597010 | semidirect |
| 107. D8 | C2×#10597010 | semidirect |
| 118. C16 | C2×#10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750672 | 2 |
| #23750666 | 2 |
| #23750550 | 2 |
| #23750543 | 2 |
| #23750541 | 2 |
| #23750516 | 2 |
| #23750059 | 2 |
| AGL(1,ℤ/16) | 149 |