Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
756 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 202 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. C2×D149⋊M16 | C2 | semidirect |
| 2. #23750611 | C2 | direct (N × H) |
| 3. C2×#18011972 | C2 | semidirect |
| 4. C2×#18011971 | C2 | semidirect |
| 8. D149⋊M16 | C22 | semidirect |
| 11. #18011972 | C22 | semidirect |
| 12. #18011971 | C22 | semidirect |
| 135. C2×C149 | #413 | semidirect |
| 139. C149 | C2×#413 | semidirect |
| 277. C2 | #23750611 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D149⋊M16 | 2 |
| #23750611 | 2 |
| C2×#18011972 | 2 |
| C2×#18011971 | 2 |
| C22×#14558736 | 2 |
| C2×#413 | 149 |