Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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. #23750028 | C2 | semidirect |
| 3. #23749998 | C2 | semidirect |
| 4. #23749973 | C2 | semidirect |
| 5. #23749971 | C2 | semidirect |
| 6. C8×#11924746 | C2 | semidirect |
| 7. #492×C149 | C2 | semidirect |
| 47. #11924746 | SD16 | semidirect |
| 57. C8×C149 | D8 | semidirect |
| 75. C149 | #1706 | semidirect |
| 80. #492 | D149 | semidirect |
| 133. C8 | #14558721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750028 | 2 |
| #23750001 | 2 |
| #23749998 | 2 |
| #23749973 | 2 |
| #23749971 | 2 |
| C8×#11924746 | 2 |
| #492×C149 | 2 |
| #1706 | 149 |