Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
572 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 153 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×#18011933 | C2 | semidirect |
| 2. C2×#18011931 | C2 | semidirect |
| 3. #23750171 | C2 | semidirect |
| 4. #23750010 | C2 | semidirect |
| 5. #23750008 | C2 | semidirect |
| 6. #23750006 | C2 | semidirect |
| 7. #23750003 | C2 | semidirect |
| 8. #23750000 | C2 | semidirect |
| 9. #23749996 | C2 | semidirect |
| 10. C2×C8×Dic149 | C2 | semidirect |
| 11. C2×#135×C149 | C2 | semidirect |
| 55. C2×#11924746 | D4 | semidirect |
| 74. C2×C8×C149 | D4 | semidirect |
| 119. Dic149 | #135 | semidirect |
| 125. C149 | #3147 | semidirect |
| 129. C2×#135 | D149 | semidirect |
| 194. C2×C8 | C22⋊D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011933 | 2 |
| C2×#18011931 | 2 |
| #23750171 | 2 |
| #23750010 | 2 |
| #23750008 | 2 |
| #23750006 | 2 |
| #23750003 | 2 |
| #23750000 | 2 |
| #23749996 | 2 |
| C2×C8×Dic149 | 2 |
| C2×#135×C149 | 2 |
| #3147 | 149 |