Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 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. D149⋊M32 | C2 | semidirect |
| 2. C2×#18011979 | C2 | semidirect |
| 3. #23750542 | C2 | semidirect |
| 4. #23750541 | C2 | semidirect |
| 7. #18011986 | C22 | semidirect |
| 11. #18011979 | C22 | semidirect |
| 14. #18011933 | C4 | semidirect |
| 18. Q16×D149 | C4 | semidirect |
| 20. D8×D149 | C4 | semidirect |
| 22. #135×C149 | C4 | semidirect |
| 37. Dic596 | C2×C4 | semidirect |
| 42. D1192 | C2×C4 | semidirect |
| 50. Q16×C149 | C2×C4 | semidirect |
| 52. D8×C149 | C2×C4 | semidirect |
| 102. D149 | #360 | semidirect |
| 103. C149 | C2×#360 | semidirect |
| 116. #135 | #10597010 | semidirect |
| 141. Q16 | C2×#10597010 | semidirect |
| 148. D8 | C2×#10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D149⋊M32 | 2 |
| C2×#18011979 | 2 |
| #23750542 | 2 |
| #23750541 | 2 |
| #135×D149 | 2 |
| C2×#360 | 149 |