Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
356 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 139 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. #23750028 | C2 | semidirect |
| 3. #23749960 | C2 | semidirect |
| 4. #23749958 | C2 | semidirect |
| 5. #23749920 | C2 | semidirect |
| 6. #23749917 | C2 | semidirect |
| 7. #23749864 | C2 | semidirect |
| 8. C4×#14558726 | C2 | semidirect |
| 10. C2×#18011844 | C2 | semidirect |
| 87. D4×C149 | Q16 | semidirect |
| 117. C149 | #3338 | semidirect |
| 198. D4 | #14558726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750332 | 2 |
| #23750028 | 2 |
| #23749960 | 2 |
| #23749958 | 2 |
| #23749920 | 2 |
| #23749917 | 2 |
| #23749864 | 2 |
| C4×#14558726 | 2 |
| D4×#11924746 | 2 |
| C2×#18011844 | 2 |
| #554×C149 | 2 |
| #3338 | 149 |