Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
1736 conjugacy classes of subgroups; only the 581 normal subgroups are shown.
This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 581 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. C22×#14558737 | C2 | semidirect |
| 2. #23750297 | C2 | direct (N × H) |
| 3. C2×#18011908 | C2 | semidirect |
| 4. C2×#18011886 | C2 | semidirect |
| 5. C2×C4×D596 | C2 | semidirect |
| 6. C2×C4×Q8×C149 | C2 | semidirect |
| 8. C2×#14558737 | C22 | semidirect |
| 13. #18011908 | C22 | semidirect |
| 14. #18011886 | C22 | semidirect |
| 15. C4×D596 | C22 | semidirect |
| 19. C4×Q8×C149 | C22 | semidirect |
| 35. C2×Q8×C149 | D4 | semidirect |
| 53. Q8×C149 | C2×D4 | semidirect |
| 56. C2×C4×C149 | #41 | semidirect |
| 70. C4×C149 | C2×#41 | semidirect |
| 72. C2×C149 | #550 | semidirect |
| 77. C149 | C2×#550 | semidirect |
| 83. C2×C4×Q8 | D149 | semidirect |
| 94. C4×Q8 | C2×D149 | semidirect |
| 102. C2×Q8 | D596 | semidirect |
| 125. Q8 | C2×D596 | semidirect |
| 134. C2×C4 | #14558737 | semidirect |
| 149. C4 | C2×#14558737 | semidirect |
| 151. C2 | #23750297 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558737 | 2 |
| #23750297 | 2 |
| C2×#18011908 | 2 |
| C2×#18011886 | 2 |
| C2×C4×D596 | 2 |
| C2×C4×Q8×C149 | 2 |
| C2×#550 | 149 |