Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
| 2. #23750348 | C2 | semidirect |
| 3. #23750009 | C2 | semidirect |
| 4. #23749998 | C2 | semidirect |
| 5. #23749848 | C2 | semidirect |
| 6. #23749841 | C2 | semidirect |
| 7. #23749836 | C2 | semidirect |
| 9. C4×#14558725 | C2 | semidirect |
| 10. C4×#14558725 | C2 | semidirect |
| 11. C8×Q8×C149 | C2 | semidirect |
| 125. C149 | #3394 | semidirect |
| 135. C8×Q8 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750360 | 2 |
| #23750348 | 2 |
| #23750009 | 2 |
| #23749998 | 2 |
| #23749848 | 2 |
| #23749841 | 2 |
| #23749836 | 2 |
| #23749821 | 2 |
| C4×#14558725 | 2 |
| C8×Q8×C149 | 2 |
| #3394 | 149 |