Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
144 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×#18011856 | C2 | semidirect |
| 2. #23750041 | C2 | semidirect |
| 3. #23749901 | C2 | semidirect |
| 5. #23749440 | C2 | semidirect |
| 6. #23749437 | C2 | semidirect |
| 7. #368×C149 | C2 | semidirect |
| 71. C149 | #2223 | semidirect |
| 77. #368 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011856 | 2 |
| #23750041 | 2 |
| #23749901 | 2 |
| #23749896 | 2 |
| #23749440 | 2 |
| #23749437 | 2 |
| #368×C149 | 2 |
| #2223 | 149 |