Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23750336 | C2 | semidirect |
| 2. #23750290 | C2 | semidirect |
| 3. #23750032 | C2 | semidirect |
| 4. #23749924 | C2 | semidirect |
| 5. #23749914 | C2 | semidirect |
| 6. #23749912 | C2 | semidirect |
| 7. #23749902 | C2 | semidirect |
| 8. #23749755 | C2 | semidirect |
| 11. #498×C149 | C2 | semidirect |
| 50. D1192 | Q8 | semidirect |
| 80. D596 | C2×Q8 | semidirect |
| 98. C8×C149 | C2×Q8 | semidirect |
| 121. C149 | #3384 | semidirect |
| 126. #498 | D149 | semidirect |
| 220. C8 | Q8×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750336 | 2 |
| #23750290 | 2 |
| #23750032 | 2 |
| #23749924 | 2 |
| #23749914 | 2 |
| #23749912 | 2 |
| #23749902 | 2 |
| #23749755 | 2 |
| #23749736 | 2 |
| C4×D1192 | 2 |
| #498×C149 | 2 |
| #3384 | 149 |