Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
540 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 540 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. #23749529 | C2 | semidirect |
| 3. #23749517 | C2 | semidirect |
| 4. #23749514 | C2 | semidirect |
| 6. #23749499 | C2 | semidirect |
| 7. C4×C4⋊Dic149 | C2 | semidirect |
| 8. #23749472 | C2 | semidirect |
| 9. #383×C149 | C2 | semidirect |
| 13. #18011899 | C4 | semidirect |
| 34. C2×Dic298 | C2×C4 | semidirect |
| 48. #14558713 | C2×C4 | semidirect |
| 49. #14558713 | C2×C4 | semidirect |
| 58. C42×C149 | C2×C4 | semidirect |
| 118. C149 | #2337 | semidirect |
| 126. #383 | D149 | semidirect |
| 177. C42 | C4×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011899 | 2 |
| #23749529 | 2 |
| #23749517 | 2 |
| #23749514 | 2 |
| #23749503 | 2 |
| #23749499 | 2 |
| C4×C4⋊Dic149 | 2 |
| #23749472 | 2 |
| #383×C149 | 2 |
| #2337 | 149 |