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×#18011934 | C2 | semidirect |
| 2. C2×#18011930 | C2 | semidirect |
| 3. #23750056 | C2 | direct (N × H) |
| 4. C2×#18011857 | C2 | semidirect |
| 5. C2×#18011856 | C2 | semidirect |
| 6. C2×#18011852 | C2 | semidirect |
| 7. C2×C16×D149 | C2 | semidirect |
| 8. C2×SD32×C149 | C2 | semidirect |
| 12. #18011934 | C22 | semidirect |
| 14. #18011930 | C22 | semidirect |
| 20. #18011857 | C22 | semidirect |
| 21. #18011856 | C22 | semidirect |
| 22. #18011852 | C22 | semidirect |
| 24. C16×D149 | C22 | semidirect |
| 27. SD32×C149 | C22 | semidirect |
| 95. C2×C149 | #508 | semidirect |
| 99. C149 | C2×#508 | semidirect |
| 106. C2×SD32 | D149 | semidirect |
| 124. SD32 | C2×D149 | semidirect |
| 197. C2 | #23750056 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011934 | 2 |
| C2×#18011930 | 2 |
| #23750056 | 2 |
| C2×#18011857 | 2 |
| C2×#18011856 | 2 |
| C2×#18011852 | 2 |
| C2×C16×D149 | 2 |
| C2×SD32×C149 | 2 |
| C2×#508 | 149 |