Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#18011944 | C2 | semidirect |
| 3. C2×#18011890 | C2 | semidirect |
| 4. #23749789 | C2 | semidirect |
| 5. #23749783 | C2 | semidirect |
| 6. #23749778 | C2 | semidirect |
| 7. #23749627 | C2 | semidirect |
| 8. #407×C149 | C2 | semidirect |
| 15. C22×Dic298 | C22 | semidirect |
| 20. C2×Dic596 | C22 | semidirect |
| 21. C2×#14558725 | C22 | semidirect |
| 25. #18011890 | C22 | semidirect |
| 26. C2×C4⋊Dic149 | C22 | semidirect |
| 29. #18011836 | C22 | semidirect |
| 30. #18011833 | C22 | semidirect |
| 32. C2×M16×C149 | C22 | semidirect |
| 34. C22⋊C8×C149 | C22 | semidirect |
| 126. C22×C149 | #137 | semidirect |
| 146. C149 | #3007 | semidirect |
| 155. #407 | D149 | semidirect |
| 170. C2×M16 | C2×D149 | semidirect |
| 181. C22⋊C8 | C2×D149 | semidirect |
| 277. C22 | #18011944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558736 | 2 |
| C2×#18011944 | 2 |
| C2×#18011890 | 2 |
| #23749789 | 2 |
| #23749783 | 2 |
| #23749778 | 2 |
| #23749627 | 2 |
| #407×C149 | 2 |
| #3007 | 149 |