Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
348 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 112 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. C2×#18011966 | C2 | semidirect |
| 4. C2×C4×#11924753 | C2 | semidirect |
| 5. #23750491 | C2 | semidirect |
| 6. #23750491 | C2 | semidirect |
| 10. C2×#14558745 | C4 | semidirect |
| 15. C22⋊#11924753 | C4 | semidirect |
| 60. #11924753 | C22⋊C4 | semidirect |
| 73. C2×Dic149 | M16 | semidirect |
| 93. C2×C4×C149 | M16 | semidirect |
| 125. C149 | #1753 | semidirect |
| 215. C2×C4 | #14558745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558745 | 2 |
| C2×C22⋊#11924753 | 2 |
| C2×#18011966 | 2 |
| C2×C4×#11924753 | 2 |
| #23750491 | 2 |
| C22⋊C4×Dic149 | 2 |
| #1753 | 149 |