Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
176 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 176 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. #23749912 | C2 | semidirect |
| 3. C8×D596 | C2 | semidirect |
| 4. #23749376 | C2 | semidirect |
| 5. #23749374 | C2 | semidirect |
| 6. #23749369 | C2 | semidirect |
| 7. #486×C149 | C2 | semidirect |
| 82. C149 | #1677 | semidirect |
| 84. #486 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23749912 | 2 |
| #23749817 | 2 |
| C8×D596 | 2 |
| #23749376 | 2 |
| #23749374 | 2 |
| #23749369 | 2 |
| #486×C149 | 2 |
| #1677 | 149 |