Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 2. C22×#14558720 | C2 | semidirect |
| 3. #23749624 | C2 | direct (N × H) |
| 4. C2×#18011834 | C2 | semidirect |
| 5. C2×#18011831 | C2 | semidirect |
| 6. C22×C4⋊C4×C149 | C2 | semidirect |
| 9. C2×#14558736 | C4 | semidirect |
| 16. C2×#14558720 | C22 | semidirect |
| 18. #18011834 | C22 | semidirect |
| 19. #18011831 | C22 | semidirect |
| 25. C2×C4⋊C4×C149 | C22 | semidirect |
| 29. #14558736 | C2×C4 | semidirect |
| 32. C2×Dic298 | C2×C4 | semidirect |
| 36. C2×D596 | C2×C4 | semidirect |
| 65. Dic298 | C22×C4 | semidirect |
| 68. D596 | C22×C4 | semidirect |
| 110. C2×C149 | #417 | semidirect |
| 115. C149 | C2×#417 | semidirect |
| 119. C22×C4⋊C4 | D149 | semidirect |
| 139. C2×C4⋊C4 | C2×D149 | semidirect |
| 227. C2 | #23749624 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558736 | 2 |
| C22×#14558720 | 2 |
| #23749624 | 2 |
| C2×#18011834 | 2 |
| C2×#18011831 | 2 |
| C22×C4⋊C4×C149 | 2 |
| C2×#417 | 149 |