Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23753029 | C2 | semidirect |
| 2. #23753022 | C2 | semidirect |
| 3. #23753013 | C2 | semidirect |
| 4. #23752595 | C2 | semidirect |
| 5. #23752488 | C2 | semidirect |
| 6. #23752474 | C2 | semidirect |
| 7. #23752392 | C2 | semidirect |
| 8. #23752383 | C2 | semidirect |
| 9. #23752328 | C2 | semidirect |
| 10. #23752327 | C2 | semidirect |
| 11. #472×C151 | C2 | semidirect |
| 12. #18012786 | C22 | semidirect |
| 16. #18012772 | C22 | semidirect |
| 27. C2×Dic604 | C22 | semidirect |
| 28. C2×#14558992 | C22 | semidirect |
| 31. #18012747 | C22 | semidirect |
| 33. #18012726 | C22 | semidirect |
| 34. #18012674 | C22 | semidirect |
| 35. #18012666 | C22 | semidirect |
| 37. #18012665 | C22 | semidirect |
| 38. #18012657 | C22 | semidirect |
| 39. C8×Dic151 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C151 | C22 | semidirect |
| 42. #131×C151 | C22 | semidirect |
| 43. #108×C151 | C22 | semidirect |
| 44. #100×C151 | C22 | semidirect |
| 149. C151 | #3290 | semidirect |
| 156. #472 | D151 | semidirect |
| 171. AGL(1,ℤ/8) | C2×D151 | semidirect |
| 185. #131 | C2×D151 | semidirect |
| 188. #108 | C2×D151 | semidirect |
| 193. #100 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23753029 | 2 |
| #23753022 | 2 |
| #23753013 | 2 |
| #23752595 | 2 |
| #23752488 | 2 |
| #23752474 | 2 |
| #23752392 | 2 |
| #23752383 | 2 |
| #23752328 | 2 |
| #23752327 | 2 |
| #472×C151 | 2 |
| #3290 | 151 |