Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23750345 | C2 | semidirect |
| 3. #23750006 | C2 | semidirect |
| 4. #23749998 | C2 | semidirect |
| 5. #23749850 | C2 | semidirect |
| 6. #23749839 | C2 | semidirect |
| 7. #23749835 | C2 | semidirect |
| 9. C8×Dic298 | C2 | semidirect |
| 10. #23749712 | C2 | semidirect |
| 11. C4×SD16×C149 | C2 | semidirect |
| 125. C149 | #3394 | semidirect |
| 137. C4×SD16 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750360 | 2 |
| #23750345 | 2 |
| #23750006 | 2 |
| #23749998 | 2 |
| #23749850 | 2 |
| #23749839 | 2 |
| #23749835 | 2 |
| #23749820 | 2 |
| C8×Dic298 | 2 |
| #23749712 | 2 |
| C4×SD16×C149 | 2 |
| #3394 | 149 |