Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#18012761 | C2 | semidirect |
| 2. #23752723 | C2 | semidirect |
| 3. #23752470 | C2 | semidirect |
| 4. #23752465 | C2 | semidirect |
| 5. #23752458 | C2 | semidirect |
| 6. #23752250 | C2 | semidirect |
| 7. #23752209 | C2 | semidirect |
| 8. C22×M16×C151 | C2 | semidirect |
| 11. C2×Dic604 | C22 | semidirect |
| 12. C2×#14558993 | C22 | semidirect |
| 13. C2×D1208 | C22 | semidirect |
| 20. #18012673 | C22 | semidirect |
| 21. #18012671 | C22 | semidirect |
| 22. #18012664 | C22 | semidirect |
| 23. #18012661 | C22 | semidirect |
| 56. C2×C8×C151 | D4 | semidirect |
| 105. C151 | #3054 | semidirect |
| 108. C22×M16 | D151 | semidirect |
| 156. C2×C8 | C22⋊D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012761 | 2 |
| #23752723 | 2 |
| #23752470 | 2 |
| #23752465 | 2 |
| #23752458 | 2 |
| #23752250 | 2 |
| #23752209 | 2 |
| C22×M16×C151 | 2 |
| #3054 | 151 |