Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#14558726 | C2 | semidirect |
| 3. #23750004 | C2 | semidirect |
| 4. #23749864 | C2 | semidirect |
| 5. #23749835 | C2 | semidirect |
| 6. #23749832 | C2 | semidirect |
| 7. #23749781 | C2 | semidirect |
| 8. #23749780 | C2 | semidirect |
| 9. C4×#14558726 | C2 | semidirect |
| 52. #14558726 | D4 | direct (N × H) |
| 100. D4×C149 | Q16 | semidirect |
| 113. C22×C149 | C2×Q16 | semidirect |
| 120. C4×C149 | C2×Q16 | semidirect |
| 130. C149 | D4×Q16 | semidirect |
| 224. D4 | #14558726 | direct (N × H) |
| 244. C22 | C2×#14558726 | semidirect |
| 254. C4 | C2×#14558726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558726 | 2 |
| D4×Dic298 | 2 |
| #23750004 | 2 |
| #23749864 | 2 |
| #23749835 | 2 |
| #23749832 | 2 |
| #23749781 | 2 |
| #23749780 | 2 |
| C4×#14558726 | 2 |
| D4×#11924746 | 2 |
| D4×Q8×C149 | 2 |
| D4×Q16 | 149 |