Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
220 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 1. #23750430 | C2 | semidirect |
| 2. #23750061 | C2 | semidirect |
| 3. C2×#18011852 | C2 | semidirect |
| 4. #23749437 | C2 | semidirect |
| 5. #23749431 | C2 | semidirect |
| 6. #23749409 | C2 | semidirect |
| 7. #472×C149 | C2 | semidirect |
| 18. #18011851 | C22 | semidirect |
| 19. C2×#14558711 | C22 | semidirect |
| 21. C2×D8×C149 | C22 | semidirect |
| 23. #108×C149 | C22 | semidirect |
| 93. C149 | #2192 | semidirect |
| 98. #472 | D149 | semidirect |
| 110. C2×D8 | C2×D149 | semidirect |
| 117. #108 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750430 | 2 |
| #23750061 | 2 |
| C2×#18011852 | 2 |
| #23749437 | 2 |
| #23749431 | 2 |
| #23749409 | 2 |
| #472×C149 | 2 |
| #2192 | 149 |