Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23750335 | C2 | semidirect |
| 2. #23750031 | C2 | semidirect |
| 3. #23750021 | C2 | semidirect |
| 4. #23749925 | C2 | semidirect |
| 5. #23749915 | C2 | semidirect |
| 6. #23749912 | C2 | semidirect |
| 7. #23749902 | C2 | semidirect |
| 8. #23749756 | C2 | semidirect |
| 11. D4×Q8×C149 | C2 | semidirect |
| 45. #14558721 | Q8 | semidirect |
| 76. D596 | C2×Q8 | semidirect |
| 83. #11924746 | C2×Q8 | semidirect |
| 121. C149 | #3384 | semidirect |
| 124. D4×Q8 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750335 | 2 |
| #23750031 | 2 |
| #23750021 | 2 |
| #23749925 | 2 |
| #23749915 | 2 |
| #23749912 | 2 |
| #23749902 | 2 |
| #23749756 | 2 |
| #23749735 | 2 |
| C4×#14558721 | 2 |
| D4×Q8×C149 | 2 |
| #3384 | 149 |