Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23750002 | C2 | semidirect |
| 3. #23749821 | C2 | semidirect |
| 4. C4×D1192 | C2 | semidirect |
| 5. C8×Q8×C149 | C2 | semidirect |
| 38. Q8×C149 | D8 | semidirect |
| 43. C8×C149 | #41 | semidirect |
| 57. C149 | #3391 | semidirect |
| 62. C8×Q8 | D149 | semidirect |
| 90. Q8 | D1192 | semidirect |
| 101. C8 | #14558737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750297 | 2 |
| #23750002 | 2 |
| #23749821 | 2 |
| C4×D1192 | 2 |
| C8×Q8×C149 | 2 |
| #3391 | 149 |