Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 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. #23752769 | C2 | semidirect |
| 3. #23752585 | C2 | semidirect |
| 4. #23752559 | C2 | semidirect |
| 5. #23752413 | C2 | semidirect |
| 6. #23752365 | C2 | semidirect |
| 7. #431×C151 | C2 | semidirect |
| 11. C2×#14558993 | C22 | semidirect |
| 12. #18012739 | C22 | semidirect |
| 13. #18012739 | C22 | semidirect |
| 22. C4×Dic302 | C22 | semidirect |
| 24. #18012661 | C22 | semidirect |
| 26. C4⋊C8×C151 | C22 | semidirect |
| 28. C4×C8×C151 | C22 | semidirect |
| 75. C2×C4×C151 | SD16 | semidirect |
| 104. C151 | #3208 | semidirect |
| 112. #431 | D151 | semidirect |
| 130. C4⋊C8 | C2×D151 | semidirect |
| 133. C4×C8 | C2×D151 | semidirect |
| 180. C2×C4 | #14558993 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752769 | 2 |
| C2×#18012736 | 2 |
| #23752585 | 2 |
| #23752559 | 2 |
| #23752413 | 2 |
| #23752365 | 2 |
| #431×C151 | 2 |
| #3208 | 151 |