Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
368 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 368 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. #23750684 | C2 | direct (N × H) |
| 2. C2×#18011986 | C2 | semidirect |
| 3. C2×#18011985 | C2 | semidirect |
| 4. C2×D149⋊C16 | C2 | semidirect |
| 5. C22×#14558739 | C2 | semidirect |
| 7. #18011986 | C22 | semidirect |
| 8. #18011985 | C22 | semidirect |
| 9. D149⋊C16 | C22 | semidirect |
| 13. C2×#14558739 | C22 | semidirect |
| 66. C2×C149 | #504 | semidirect |
| 69. C149 | C2×#504 | semidirect |
| 137. C2 | #23750684 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750684 | 2 |
| C2×#18011986 | 2 |
| C2×#18011985 | 2 |
| C2×D149⋊C16 | 2 |
| C22×#14558739 | 2 |
| C2×#18011919 | 2 |
| C2×#504 | 149 |