Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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×#18012727 | C2 | semidirect |
| 2. #23752599 | C2 | semidirect |
| 3. #23752574 | C2 | semidirect |
| 4. #23752427 | C2 | semidirect |
| 5. #23752350 | C2 | semidirect |
| 6. #23752345 | C2 | semidirect |
| 7. #23752269 | C2 | semidirect |
| 8. #532×C151 | C2 | semidirect |
| 11. C2×#14558992 | C22 | semidirect |
| 19. C4⋊(C151⋊C8) | C22 | semidirect |
| 20. #18012662 | C22 | semidirect |
| 23. #18012650 | C22 | semidirect |
| 25. C4⋊Q8×C151 | C22 | semidirect |
| 26. #127×C151 | C22 | semidirect |
| 31. C4×D4×C151 | C22 | semidirect |
| 120. C151 | #3213 | semidirect |
| 122. #532 | D151 | semidirect |
| 135. C4⋊Q8 | C2×D151 | semidirect |
| 136. #127 | C2×D151 | semidirect |
| 145. C4×D4 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012727 | 2 |
| #23752599 | 2 |
| #23752574 | 2 |
| #23752427 | 2 |
| #23752350 | 2 |
| #23752345 | 2 |
| #23752269 | 2 |
| #532×C151 | 2 |
| #3213 | 151 |