Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
1008 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 234 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×#14558745 | C2 | semidirect |
| 2. #23750597 | C2 | direct (N × H) |
| 3. C2×#18011968 | C2 | semidirect |
| 6. C2×#14558745 | C22 | semidirect |
| 7. C22×#11924753 | C22 | semidirect |
| 8. #18011968 | C22 | semidirect |
| 19. C2×#11924753 | C23 | semidirect |
| 46. C22×D149 | M16 | semidirect |
| 75. C2×D149 | C2×M16 | semidirect |
| 81. C2×C149 | #407 | semidirect |
| 85. C149 | C2×#407 | semidirect |
| 168. C2 | #23750597 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558745 | 2 |
| #23750597 | 2 |
| C2×#18011968 | 2 |
| C23×C4×D149 | 2 |
| C2×#407 | 149 |