Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
112 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 35 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. #23750058 | C2 | semidirect |
| 2. D16×D149 | C2 | semidirect |
| 3. #23749462 | C2 | semidirect |
| 4. D4768 | C2 | semidirect |
| 5. #23749460 | C2 | semidirect |
| 6. #23749458 | C2 | semidirect |
| 7. SD64×C149 | C2 | semidirect |
| 12. D2384 | C22 | semidirect |
| 15. #18011817 | C22 | semidirect |
| 16. Q32×C149 | C22 | semidirect |
| 18. C32×C149 | C22 | semidirect |
| 54. C149 | #2263 | semidirect |
| 59. SD64 | D149 | semidirect |
| 65. Q32 | C2×D149 | semidirect |
| 73. C32 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750058 | 2 |
| D16×D149 | 2 |
| #23749462 | 2 |
| D4768 | 2 |
| #23749460 | 2 |
| #23749458 | 2 |
| SD64×C149 | 2 |
| #2263 | 149 |