Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
126 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 45 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. #23750022 | C2 | semidirect |
| 3. #23749448 | C2 | semidirect |
| 4. #23749447 | C2 | semidirect |
| 5. #23749445 | C2 | semidirect |
| 29. Q16×C149 | Q8 | semidirect |
| 31. D8×C149 | Q8 | semidirect |
| 60. C149 | #2230 | semidirect |
| 82. Q16 | Dic298 | semidirect |
| 84. D8 | Dic298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750022 | 2 |
| #23749742 | 2 |
| #23749448 | 2 |
| #23749447 | 2 |
| #23749445 | 2 |
| #23749435 | 2 |
| #360×C149 | 2 |
| #2230 | 149 |