Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
426 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 426 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 |
|---|---|---|
| 1. #23750297 | C2 | semidirect |
| 2. Q8×D596 | C2 | semidirect |
| 3. #23749972 | C2 | semidirect |
| 4. #23749906 | C2 | semidirect |
| 5. #23749821 | C2 | semidirect |
| 6. C4×D1192 | C2 | semidirect |
| 7. C8×Q8×C149 | C2 | semidirect |
| 52. D596 | #41 | semidirect |
| 57. Q8×C149 | D8 | semidirect |
| 81. C149 | #3358 | semidirect |
| 88. C8×Q8 | D149 | semidirect |
| 129. Q8 | D1192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750297 | 2 |
| Q8×D596 | 2 |
| #23749972 | 2 |
| #23749906 | 2 |
| #23749821 | 2 |
| C4×D1192 | 2 |
| C8×Q8×C149 | 2 |
| #3358 | 149 |