Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23752865 | C2 | semidirect |
| 2. D4×D604 | C2 | semidirect |
| 3. #23752560 | C2 | semidirect |
| 4. #23752527 | C2 | semidirect |
| 5. #23752449 | C2 | semidirect |
| 6. #23752408 | C2 | semidirect |
| 7. #23752347 | C2 | semidirect |
| 8. C4×#14558989 | C2 | semidirect |
| 9. #23752277 | C2 | semidirect |
| 10. #102×D151 | C2 | semidirect |
| 11. #474×C151 | C2 | semidirect |
| 15. C2×D1208 | C22 | semidirect |
| 17. C2×C8×D151 | C22 | semidirect |
| 22. #18012714 | C22 | semidirect |
| 26. C4×D604 | C22 | semidirect |
| 27. C4⋊C4×D151 | C22 | semidirect |
| 28. #18012672 | C22 | semidirect |
| 29. #18012661 | C22 | semidirect |
| 31. #18012659 | C22 | semidirect |
| 32. #18012659 | C22 | semidirect |
| 33. #18012659 | C22 | semidirect |
| 34. (C2×D151)⋊C8 | C22 | semidirect |
| 35. C4×C151⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C151 | C22 | semidirect |
| 38. #107×C151 | C22 | semidirect |
| 39. C4⋊C8×C151 | C22 | semidirect |
| 92. D604 | D8 | semidirect |
| 105. D4×C151 | #41 | semidirect |
| 142. C151 | #3294 | semidirect |
| 148. #474 | D151 | semidirect |
| 161. C4⋊Q8 | C2×D151 | semidirect |
| 174. #107 | C2×D151 | semidirect |
| 175. C4⋊C8 | C2×D151 | semidirect |
| 240. D4 | #14559005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752865 | 2 |
| D4×D604 | 2 |
| #23752560 | 2 |
| #23752527 | 2 |
| #23752449 | 2 |
| #23752408 | 2 |
| #23752347 | 2 |
| C4×#14558989 | 2 |
| #23752277 | 2 |
| #102×D151 | 2 |
| #474×C151 | 2 |
| #3294 | 151 |