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. #23752762 | C2 | semidirect |
| 2. C2×#18012736 | C2 | semidirect |
| 3. #23752589 | C2 | semidirect |
| 4. #23752559 | C2 | semidirect |
| 5. #23752408 | C2 | semidirect |
| 6. #23752348 | C2 | semidirect |
| 7. #431×C151 | C2 | semidirect |
| 12. C2×D1208 | C22 | semidirect |
| 13. #18012739 | C22 | semidirect |
| 18. #18012736 | C22 | semidirect |
| 23. C4×D604 | C22 | semidirect |
| 24. #18012661 | C22 | semidirect |
| 26. C4⋊C8×C151 | C22 | semidirect |
| 28. C4×C8×C151 | C22 | semidirect |
| 80. C2×C4×C151 | D8 | semidirect |
| 112. C151 | #3205 | semidirect |
| 120. #431 | D151 | semidirect |
| 138. C4⋊C8 | C2×D151 | semidirect |
| 141. C4×C8 | C2×D151 | semidirect |
| 193. C2×C4 | D1208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752762 | 2 |
| C2×#18012736 | 2 |
| #23752589 | 2 |
| #23752559 | 2 |
| #23752408 | 2 |
| #23752348 | 2 |
| #431×C151 | 2 |
| #3205 | 151 |