Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
320 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. M16×#10597010 | C2 | semidirect |
| 4. #23750561 | C2 | semidirect |
| 5. #23750497 | C2 | semidirect |
| 6. #23750496 | C2 | semidirect |
| 9. Q8×#10597010 | C4 | semidirect |
| 11. D4×#10597010 | C4 | semidirect |
| 17. #18011976 | C4 | semidirect |
| 18. #18011975 | C4 | semidirect |
| 25. #18011839 | C4 | semidirect |
| 26. #18011838 | C4 | semidirect |
| 27. #18011837 | C4 | semidirect |
| 28. #104×C149 | C4 | semidirect |
| 32. #14558746 | C2×C4 | semidirect |
| 43. C4×#10597010 | C2×C4 | semidirect |
| 57. #14558720 | C2×C4 | semidirect |
| 61. C4×Dic149 | C2×C4 | semidirect |
| 63. M16×C149 | C2×C4 | semidirect |
| 64. C42×C149 | C2×C4 | semidirect |
| 126. C149 | #1759 | semidirect |
| 152. #104 | #10597010 | semidirect |
| 175. M16 | C2×#10597010 | semidirect |
| 191. C42 | C2×#10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#10597010 | 2 |
| D149⋊#104 | 2 |
| M16×#10597010 | 2 |
| #23750561 | 2 |
| #23750497 | 2 |
| #23750496 | 2 |
| #104×D149 | 2 |
| #1759 | 149 |