Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
162 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 162 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. Q16×#10597010 | C2 | semidirect |
| 3. #23750552 | C2 | semidirect |
| 4. #23750538 | C2 | semidirect |
| 6. C16×#10597010 | C2 | semidirect |
| 18. #18011856 | C4 | semidirect |
| 19. #18011855 | C4 | semidirect |
| 20. #18011854 | C4 | semidirect |
| 22. SD32×C149 | C4 | semidirect |
| 34. Dic596 | C2×C4 | semidirect |
| 39. #14558711 | C2×C4 | semidirect |
| 40. Q16×C149 | C2×C4 | semidirect |
| 42. C16×C149 | C2×C4 | semidirect |
| 68. #10597010 | SD32 | direct (N × H) |
| 78. C149 | C4×SD32 | semidirect |
| 94. SD32 | #10597010 | direct (N × H) |
| 107. Q16 | C2×#10597010 | semidirect |
| 121. C16 | C2×#10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#10597010 | 2 |
| D8×#10597010 | 2 |
| #23750552 | 2 |
| #23750538 | 2 |
| #23750537 | 2 |
| C16×#10597010 | 2 |
| SD32×D149 | 2 |
| C4×SD32 | 149 |