Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
572 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 165 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×#18012772 | C2 | semidirect |
| 2. C2×#18012767 | C2 | semidirect |
| 3. #23752762 | C2 | semidirect |
| 4. C2×#18012727 | C2 | semidirect |
| 5. #23752606 | C2 | semidirect |
| 6. #23752601 | C2 | semidirect |
| 7. #23752596 | C2 | semidirect |
| 8. C4×M16×C151 | C2 | semidirect |
| 14. C2×Dic604 | C22 | semidirect |
| 16. C2×#14558993 | C22 | semidirect |
| 18. #18012739 | C22 | semidirect |
| 19. #18012736 | C22 | semidirect |
| 23. #18012727 | C22 | semidirect |
| 29. #97×C151 | C22 | semidirect |
| 30. C4×C8×C151 | C22 | semidirect |
| 56. M16×C151 | D4 | semidirect |
| 106. C151 | #3153 | semidirect |
| 115. C4×M16 | D151 | semidirect |
| 136. #97 | C2×D151 | semidirect |
| 137. C4×C8 | C2×D151 | semidirect |
| 159. M16 | D604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012772 | 2 |
| C2×#18012767 | 2 |
| #23752762 | 2 |
| C2×#18012727 | 2 |
| #23752606 | 2 |
| #23752601 | 2 |
| #23752596 | 2 |
| C4×M16×C151 | 2 |
| #3153 | 151 |