Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23750345 | C2 | semidirect |
| 3. #23749976 | C2 | semidirect |
| 4. #23749967 | C2 | semidirect |
| 5. #23749906 | C2 | semidirect |
| 6. #23749866 | C2 | semidirect |
| 7. #23749836 | C2 | semidirect |
| 8. #23749789 | C2 | semidirect |
| 9. C4×#14558725 | C2 | semidirect |
| 10. #23749622 | C2 | semidirect |
| 11. C8×D4×C149 | C2 | semidirect |
| 125. C149 | #3302 | semidirect |
| 136. C8×D4 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750345 | 2 |
| #23750280 | 2 |
| #23749976 | 2 |
| #23749967 | 2 |
| #23749906 | 2 |
| #23749866 | 2 |
| #23749836 | 2 |
| #23749789 | 2 |
| C4×#14558725 | 2 |
| #23749622 | 2 |
| C8×D4×C149 | 2 |
| #3302 | 149 |