Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23750172 | C2 | semidirect |
| 2. #23750029 | C2 | semidirect |
| 3. #23750000 | C2 | semidirect |
| 4. #23749970 | C2 | semidirect |
| 5. #23749862 | C2 | semidirect |
| 6. #23749860 | C2 | semidirect |
| 7. #23749858 | C2 | semidirect |
| 8. C4×D1192 | C2 | semidirect |
| 9. C4×#14558721 | C2 | semidirect |
| 10. C4×C8×D149 | C2 | semidirect |
| 11. C4×D8×C149 | C2 | semidirect |
| 89. C4×D149 | D8 | semidirect |
| 91. #11924746 | #41 | semidirect |
| 101. C8×C149 | #41 | semidirect |
| 127. C149 | #3169 | semidirect |
| 138. C4×D8 | D149 | semidirect |
| 229. C8 | #14558736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750172 | 2 |
| #23750029 | 2 |
| #23750000 | 2 |
| #23749970 | 2 |
| #23749862 | 2 |
| #23749860 | 2 |
| #23749858 | 2 |
| C4×D1192 | 2 |
| C4×#14558721 | 2 |
| C4×C8×D149 | 2 |
| C4×D8×C149 | 2 |
| #3169 | 149 |