Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
726 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 200 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. D149⋊#131 | C2 | semidirect |
| 2. #23750694 | C2 | semidirect |
| 3. #23750618 | C2 | semidirect |
| 4. #23750616 | C2 | semidirect |
| 5. #23750615 | C2 | semidirect |
| 6. C2×#18011974 | C2 | semidirect |
| 22. #18011959 | C4 | semidirect |
| 24. #18011958 | C4 | semidirect |
| 25. #18011958 | C4 | semidirect |
| 31. 2−1+4×C149 | C4 | semidirect |
| 45. #14558737 | C2×C4 | semidirect |
| 51. #14558736 | C2×C4 | semidirect |
| 55. #14558735 | C2×C4 | semidirect |
| 59. C2×Dic298 | C2×C4 | semidirect |
| 64. Q8×D149 | C2×C4 | semidirect |
| 75. #41×C149 | C2×C4 | semidirect |
| 77. C2×Q8×C149 | C2×C4 | semidirect |
| 141. C149 | #2898 | semidirect |
| 155. 2−1+4 | #10597010 | semidirect |
| 189. #41 | C2×#10597010 | semidirect |
| 201. C2×Q8 | C2×#10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D149⋊#131 | 2 |
| #23750694 | 2 |
| #23750618 | 2 |
| #23750616 | 2 |
| #23750615 | 2 |
| C2×#18011974 | 2 |
| 2−1+4×D149 | 2 |
| #2898 | 149 |