Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 532 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. #23752762 | C2 | semidirect |
| 2. #23752588 | C2 | semidirect |
| 3. #23752558 | C2 | semidirect |
| 4. #23752404 | C2 | semidirect |
| 5. #23752346 | C2 | semidirect |
| 6. #23752265 | C2 | semidirect |
| 7. C2×#127×C151 | C2 | semidirect |
| 9. C2×#14558989 | C22 | semidirect |
| 10. #18012739 | C22 | semidirect |
| 11. #18012736 | C22 | semidirect |
| 16. C4×D604 | C22 | semidirect |
| 17. C4⋊(C151⋊C8) | C22 | semidirect |
| 18. #18012660 | C22 | semidirect |
| 20. C4×C151⋊C8 | C22 | semidirect |
| 81. C2×C4×C151 | D8 | semidirect |
| 112. C151 | #3205 | semidirect |
| 115. C2×#127 | D151 | semidirect |
| 193. C2×C4 | #14558989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752762 | 2 |
| #23752588 | 2 |
| #23752558 | 2 |
| #23752404 | 2 |
| #23752346 | 2 |
| #23752265 | 2 |
| C2×#127×C151 | 2 |
| #3205 | 151 |