Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23752525 | C2 | semidirect |
| 3. #23752492 | C2 | semidirect |
| 4. #23752407 | C2 | semidirect |
| 5. #23752346 | C2 | semidirect |
| 6. C4×#14558989 | C2 | semidirect |
| 7. #23752265 | C2 | semidirect |
| 8. C2×C4×D4×C151 | C2 | semidirect |
| 11. #18012739 | C22 | semidirect |
| 12. #18012736 | C22 | semidirect |
| 17. C4×D604 | C22 | semidirect |
| 18. #18012672 | C22 | semidirect |
| 19. C4⋊(C151⋊C8) | C22 | semidirect |
| 21. #18012659 | C22 | semidirect |
| 23. C4×C151⋊C8 | C22 | semidirect |
| 81. D4×C151 | #41 | semidirect |
| 88. C2×C4×C151 | D8 | semidirect |
| 120. C151 | #3100 | semidirect |
| 123. C2×C4×D4 | D151 | semidirect |
| 199. D4 | #14559004 | semidirect |
| 208. 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 |
| #23752525 | 2 |
| #23752492 | 2 |
| #23752407 | 2 |
| #23752346 | 2 |
| C4×#14558989 | 2 |
| #23752265 | 2 |
| C2×C4×D4×C151 | 2 |
| #3100 | 151 |