Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
596 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 177 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. #23749525 | C2 | semidirect |
| 3. #23749514 | C2 | semidirect |
| 4. #23749510 | C2 | semidirect |
| 5. #23749503 | C2 | semidirect |
| 6. #23749501 | C2 | semidirect |
| 7. C4×C22⋊Dic149 | C2 | semidirect |
| 8. #23749472 | C2 | semidirect |
| 9. #381×C149 | C2 | semidirect |
| 13. #18011885 | C4 | semidirect |
| 38. C2×C22⋊D149 | C2×C4 | semidirect |
| 45. C4⋊Dic149 | C2×C4 | semidirect |
| 51. #14558713 | C2×C4 | semidirect |
| 58. C22×C4×C149 | C2×C4 | semidirect |
| 134. C149 | #2333 | semidirect |
| 142. #381 | D149 | semidirect |
| 183. C22×C4 | C4×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011885 | 2 |
| #23749525 | 2 |
| #23749514 | 2 |
| #23749510 | 2 |
| #23749503 | 2 |
| #23749501 | 2 |
| C4×C22⋊Dic149 | 2 |
| #23749472 | 2 |
| #381×C149 | 2 |
| #2333 | 149 |