Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
296 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 9. #18011978 | C4 | semidirect |
| 10. C4⋊#11924753 | C4 | semidirect |
| 16. C4×#11924746 | C4 | semidirect |
| 17. C8×Dic149 | C4 | semidirect |
| 18. C8×Dic149 | C4 | semidirect |
| 19. C4×C8×C149 | C4 | semidirect |
| 24. C4⋊#10597010 | C8 | direct (N × H) |
| 57. #11924746 | C4⋊C4 | semidirect |
| 62. C8×C149 | C4⋊C4 | semidirect |
| 70. C4×C149 | C4×C8 | semidirect |
| 74. Dic149 | C4×C8 | semidirect |
| 82. C149 | C8×C4⋊C4 | semidirect |
| 101. C4×C8 | #10597010 | semidirect |
| 145. C8 | C4⋊#10597010 | direct (N × H) |
| 157. C4 | C8×#10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D149⋊(C4⋊C8) | 2 |
| C2×C8×#10597010 | 2 |
| C4×C4⋊#10597010 | 2 |
| (C2×#10597010)⋊C8 | 2 |
| C4×C8×D149 | 2 |
| C8×C4⋊C4 | 149 |