Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 141 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×#18011943 | C2 | semidirect |
| 2. C2×#18011940 | C2 | semidirect |
| 4. C4⋊Q8×D149 | C2 | semidirect |
| 5. #23750020 | C2 | semidirect |
| 6. #23750019 | C2 | semidirect |
| 7. #23750017 | C2 | semidirect |
| 8. #23750003 | C2 | semidirect |
| 9. #23749996 | C2 | semidirect |
| 10. #23749577 | C2 | semidirect |
| 11. #497×C149 | C2 | semidirect |
| 63. #14558719 | D4 | semidirect |
| 124. Dic149 | #137 | semidirect |
| 130. C149 | #3152 | semidirect |
| 139. #497 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011943 | 2 |
| C2×#18011940 | 2 |
| #23750174 | 2 |
| C4⋊Q8×D149 | 2 |
| #23750020 | 2 |
| #23750019 | 2 |
| #23750017 | 2 |
| #23750003 | 2 |
| #23749996 | 2 |
| #23749577 | 2 |
| #497×C149 | 2 |
| #3152 | 149 |