Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
412 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 78 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×#18011990 | C2 | semidirect |
| 2. C2×#18011973 | C2 | semidirect |
| 3. D149⋊(C22⋊C8) | C2 | semidirect |
| 4. #23750498 | C2 | semidirect |
| 17. #18011886 | C4 | semidirect |
| 18. #18011885 | C4 | semidirect |
| 21. #18011882 | C4 | semidirect |
| 24. #121×C149 | C4 | semidirect |
| 30. C4⋊#10597010 | D4 | semidirect |
| 137. C149 | #1875 | semidirect |
| 153. #121 | #10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011990 | 2 |
| C2×#18011973 | 2 |
| D149⋊(C22⋊C8) | 2 |
| #23750498 | 2 |
| #121×D149 | 2 |
| #1875 | 149 |