Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 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×#18012765 | C2 | semidirect |
| 2. C4×#14559004 | C2 | semidirect |
| 3. #23752409 | C2 | semidirect |
| 4. #23752404 | C2 | semidirect |
| 5. #23752236 | C2 | semidirect |
| 6. #23752217 | C2 | semidirect |
| 7. C2×#127×C151 | C2 | semidirect |
| 10. C2×#14558992 | C22 | semidirect |
| 11. C2×#14558989 | C22 | semidirect |
| 13. C4×Dic302 | C22 | semidirect |
| 14. C4×D604 | C22 | semidirect |
| 19. C4⋊(C151⋊C8) | C22 | semidirect |
| 20. #18012660 | C22 | semidirect |
| 28. #14559004 | D4 | semidirect |
| 59. Dic302 | C2×D4 | semidirect |
| 61. D604 | C2×D4 | semidirect |
| 94. C4×C151 | AGL(1,ℤ/8) | semidirect |
| 104. C151 | #3038 | semidirect |
| 107. C2×#127 | D151 | semidirect |
| 201. C4 | #18012765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012765 | 2 |
| C4×#14559004 | 2 |
| #23752409 | 2 |
| #23752404 | 2 |
| #23752236 | 2 |
| #23752217 | 2 |
| C2×#127×C151 | 2 |
| #3038 | 151 |