Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23749987 | C2 | semidirect |
| 3. #23749982 | C2 | semidirect |
| 4. #23749633 | C2 | semidirect |
| 6. C4×#14558720 | C2 | semidirect |
| 7. #533×C149 | C2 | semidirect |
| 15. #18011834 | C22 | semidirect |
| 17. #18011822 | C22 | semidirect |
| 18. C4×#11924746 | C22 | semidirect |
| 19. C4⋊Q8×C149 | C22 | semidirect |
| 20. #125×C149 | C22 | semidirect |
| 83. C149 | #3140 | semidirect |
| 85. #533 | D149 | semidirect |
| 95. C4⋊Q8 | C2×D149 | semidirect |
| 96. #125 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011899 | 2 |
| #23749987 | 2 |
| #23749982 | 2 |
| #23749633 | 2 |
| #23749629 | 2 |
| C4×#14558720 | 2 |
| #533×C149 | 2 |
| #3140 | 149 |