Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 141 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×#18012736 | C2 | semidirect |
| 2. #23752588 | C2 | semidirect |
| 3. #23752560 | C2 | semidirect |
| 4. #23752407 | C2 | semidirect |
| 5. #23752345 | C2 | semidirect |
| 6. #23752265 | C2 | semidirect |
| 7. #532×C151 | C2 | semidirect |
| 11. C2×#14558989 | C22 | semidirect |
| 16. C4⋊(C151⋊C8) | C22 | semidirect |
| 17. #18012659 | C22 | semidirect |
| 19. C4×C151⋊C8 | C22 | semidirect |
| 21. C4⋊Q8×C151 | C22 | semidirect |
| 22. #127×C151 | C22 | semidirect |
| 27. C4×D4×C151 | C22 | semidirect |
| 81. C2×C4×C151 | D8 | semidirect |
| 112. C151 | #3205 | semidirect |
| 114. #532 | D151 | semidirect |
| 126. C4⋊Q8 | C2×D151 | semidirect |
| 131. #127 | C2×D151 | semidirect |
| 136. C4×D4 | C2×D151 | semidirect |
| 193. C2×C4 | #14558989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012736 | 2 |
| #23752588 | 2 |
| #23752560 | 2 |
| #23752407 | 2 |
| #23752345 | 2 |
| #23752265 | 2 |
| #532×C151 | 2 |
| #3205 | 151 |