Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
196 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 66 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. #23750653 | C2 | semidirect |
| 2. #23750488 | C2 | semidirect |
| 3. #23750473 | C2 | semidirect |
| 4. C8×#11924753 | C2 | semidirect |
| 23. D1192 | C8 | semidirect |
| 32. #11924753 | D8 | semidirect |
| 35. D596 | C2×C8 | semidirect |
| 43. C8×C149 | C2×C8 | semidirect |
| 58. C149 | C8×D8 | semidirect |
| 102. C8 | D149⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750653 | 2 |
| #23750488 | 2 |
| #23750473 | 2 |
| C8×#11924753 | 2 |
| #23749707 | 2 |
| C8×D8 | 149 |