Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 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×#18011930 | C2 | semidirect |
| 2. #23750054 | C2 | direct (N × H) |
| 3. C2×Dic1192 | C2 | semidirect |
| 4. C2×#18011855 | C2 | semidirect |
| 5. C2×C16×D149 | C2 | semidirect |
| 6. C2×D16×C149 | C2 | semidirect |
| 9. #18011930 | C22 | semidirect |
| 13. Dic1192 | C22 | semidirect |
| 14. #18011855 | C22 | semidirect |
| 16. C16×D149 | C22 | semidirect |
| 18. D16×C149 | C22 | semidirect |
| 64. C2×C149 | #508 | semidirect |
| 67. C149 | C2×#508 | semidirect |
| 73. C2×D16 | D149 | semidirect |
| 84. D16 | C2×D149 | semidirect |
| 133. C2 | #23750054 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011930 | 2 |
| #23750054 | 2 |
| C2×Dic1192 | 2 |
| C2×#18011855 | 2 |
| C2×C16×D149 | 2 |
| C2×D16×C149 | 2 |
| C2×#508 | 149 |