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. #23750671 | C2 | semidirect |
| 2. #23750666 | C2 | semidirect |
| 3. #23750549 | C2 | semidirect |
| 4. #23750543 | C2 | semidirect |
| 5. #23750542 | C2 | semidirect |
| 6. #23750516 | C2 | semidirect |
| 18. #18011854 | C4 | semidirect |
| 19. D2384 | C4 | semidirect |
| 20. #18011852 | C4 | semidirect |
| 22. SD32×C149 | C4 | semidirect |
| 36. D1192 | C2×C4 | semidirect |
| 39. #14558711 | C2×C4 | semidirect |
| 40. Q16×C149 | C2×C4 | semidirect |
| 42. C16×C149 | C2×C4 | semidirect |
| 75. C149 | AGL(1,ℤ/16) | semidirect |
| 89. SD32 | #10597010 | semidirect |
| 102. Q16 | 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 |
|---|---|
| #23750671 | 2 |
| #23750666 | 2 |
| #23750549 | 2 |
| #23750543 | 2 |
| #23750542 | 2 |
| #23750516 | 2 |
| #23750062 | 2 |
| AGL(1,ℤ/16) | 149 |