Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
360 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 174 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 |
|---|---|---|
| 10. #18011966 | C4 | semidirect |
| 11. #18011965 | C4 | semidirect |
| 12. C8×#10597010 | C4 | semidirect |
| 15. #18011822 | C4 | semidirect |
| 16. #18011821 | C4 | semidirect |
| 17. #97×C149 | C4 | semidirect |
| 39. #11924753 | C42 | semidirect |
| 46. #11924746 | C42 | semidirect |
| 49. C8×C149 | C42 | semidirect |
| 55. #10597010 | #97 | direct (N × H) |
| 64. C149 | C4×#97 | semidirect |
| 81. #97 | #10597010 | direct (N × H) |
| 114. C8 | C4×#10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750584 | 2 |
| C2×#18011965 | 2 |
| C2×C8×#10597010 | 2 |
| C42×#10597010 | 2 |
| #97×D149 | 2 |
| C4×#97 | 149 |