Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 3. #23749452 | C2 | semidirect |
| 4. #23749429 | C2 | semidirect |
| 6. C4×#14558711 | C2 | semidirect |
| 7. C4×Q16×C149 | C2 | semidirect |
| 10. #18011854 | C4 | direct (N × H) |
| 27. #14558711 | C2×C4 | semidirect |
| 30. Q16×C149 | C2×C4 | semidirect |
| 59. C4×C149 | SD32 | semidirect |
| 67. C149 | C4×SD32 | semidirect |
| 70. C4×Q16 | D149 | semidirect |
| 92. Q16 | C4×D149 | semidirect |
| 128. C4 | #18011854 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011854 | 2 |
| C4×D1192 | 2 |
| #23749452 | 2 |
| #23749429 | 2 |
| #23749425 | 2 |
| C4×#14558711 | 2 |
| C4×Q16×C149 | 2 |
| C4×SD32 | 149 |