Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 2. C2×#18011876 | C2 | semidirect |
| 4. #23749530 | C2 | semidirect |
| 6. #23749515 | C2 | semidirect |
| 7. #23749496 | C2 | semidirect |
| 8. #23749471 | C2 | semidirect |
| 9. #384×C149 | C2 | semidirect |
| 13. #18011899 | C4 | semidirect |
| 33. C2×Dic298 | C2×C4 | semidirect |
| 46. #14558713 | C2×C4 | semidirect |
| 57. C42×C149 | C2×C4 | semidirect |
| 111. C149 | #2326 | semidirect |
| 120. #384 | D149 | semidirect |
| 169. C42 | C4×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011899 | 2 |
| C2×#18011876 | 2 |
| C2×#18011873 | 2 |
| #23749530 | 2 |
| #23749526 | 2 |
| #23749515 | 2 |
| #23749496 | 2 |
| #23749471 | 2 |
| #384×C149 | 2 |
| #2326 | 149 |