Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23750360 | C2 | semidirect |
| 3. #23749826 | C2 | semidirect |
| 4. #23749825 | C2 | semidirect |
| 5. #23749368 | C2 | semidirect |
| 6. #23749357 | C2 | semidirect |
| 7. Q8⋊C8×C149 | C2 | semidirect |
| 98. C149 | #1620 | semidirect |
| 106. Q8⋊C8 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750360 | 2 |
| #23750002 | 2 |
| #23749826 | 2 |
| #23749825 | 2 |
| #23749368 | 2 |
| #23749357 | 2 |
| Q8⋊C8×C149 | 2 |
| #1620 | 149 |