Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#14558726 | C2 | semidirect |
| 4. C2×#18011909 | C2 | semidirect |
| 6. #23750018 | C2 | direct (N × H) |
| 7. C2×#18011821 | C2 | semidirect |
| 8. C22×Q16×C149 | C2 | semidirect |
| 12. C2×#14558726 | C22 | semidirect |
| 19. #18011909 | C22 | semidirect |
| 25. #18011821 | C22 | semidirect |
| 29. C2×Q16×C149 | C22 | semidirect |
| 108. C2×C149 | #497 | semidirect |
| 112. C149 | C2×#497 | semidirect |
| 115. C22×Q16 | D149 | semidirect |
| 129. C2×Q16 | C2×D149 | semidirect |
| 222. C2 | #23750018 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558726 | 2 |
| C22×#14558725 | 2 |
| C22×#14558723 | 2 |
| C2×#18011909 | 2 |
| C2×#18011900 | 2 |
| #23750018 | 2 |
| C2×#18011821 | 2 |
| C22×Q16×C149 | 2 |
| C2×#497 | 149 |