Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 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. #23750182 | C2 | semidirect |
| 3. #23749998 | C2 | semidirect |
| 4. #23749972 | C2 | semidirect |
| 5. #23749826 | C2 | semidirect |
| 6. #23749778 | C2 | semidirect |
| 7. #431×C149 | C2 | semidirect |
| 11. C2×#14558725 | C22 | semidirect |
| 12. #18011911 | C22 | semidirect |
| 13. #18011911 | C22 | semidirect |
| 22. C4×Dic298 | C22 | semidirect |
| 24. #18011833 | C22 | semidirect |
| 26. C4⋊C8×C149 | C22 | semidirect |
| 28. C4×C8×C149 | C22 | semidirect |
| 75. C2×C4×C149 | SD16 | semidirect |
| 104. C149 | #3208 | semidirect |
| 112. #431 | D149 | semidirect |
| 130. C4⋊C8 | C2×D149 | semidirect |
| 133. C4×C8 | C2×D149 | semidirect |
| 180. C2×C4 | #14558725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750182 | 2 |
| C2×#18011908 | 2 |
| #23749998 | 2 |
| #23749972 | 2 |
| #23749826 | 2 |
| #23749778 | 2 |
| #431×C149 | 2 |
| #3208 | 149 |