Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 2. #23750107 | C2 | semidirect |
| 3. #23749738 | C2 | semidirect |
| 4. #23749736 | C2 | semidirect |
| 5. #23749732 | C2 | semidirect |
| 6. C4×#14558723 | C2 | semidirect |
| 7. #23749710 | C2 | semidirect |
| 8. #106×D149 | C2 | semidirect |
| 9. #23749625 | C2 | semidirect |
| 10. #23749582 | C2 | semidirect |
| 11. #441×C149 | C2 | semidirect |
| 13. #18011934 | C4 | semidirect |
| 41. #14558737 | C2×C4 | semidirect |
| 49. #14558723 | C2×C4 | semidirect |
| 50. D1192 | C2×C4 | semidirect |
| 54. C8×D149 | C2×C4 | semidirect |
| 65. Q16×C149 | C2×C4 | semidirect |
| 114. C149 | #2952 | semidirect |
| 121. #441 | D149 | semidirect |
| 165. Q16 | C4×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011934 | 2 |
| #23750107 | 2 |
| #23749738 | 2 |
| #23749736 | 2 |
| #23749732 | 2 |
| C4×#14558723 | 2 |
| #23749710 | 2 |
| #106×D149 | 2 |
| #23749625 | 2 |
| #23749582 | 2 |
| #441×C149 | 2 |
| #2952 | 149 |